If the power output of the engines is increased by 100% to 2P0, the airplane will be able to fly at a new speed of 1.26[tex]v_{0}[/tex].
As, P = F v
So, P = kv³
Then, v/v0 = [tex]\sqrt[3]{P/P0}[/tex].
Therefore, after substituting the values, the speed will be 1.26[tex]v_{0}[/tex].
What is power?
In physics, power is the amount of energy transferred or converted per unit of time. In the International System of Units, the unit of power is the watt, which is equivalent to 1 joule per second. In older works, force is sometimes called activity. Power is a scalar quantity.
Power is related to other quantities. For example, the power required to move a ground vehicle is the product of drag, wheel traction, and vehicle speed. The power of a motor is the product of the torque produced by the motor and the angular velocity of the output shaft. Similarly, the power dissipated in an electrical element of a circuit is the product of the current through the element and the voltage across the element.
If the power output of the engines is increased by 100% to 2P0, the airplane will be able to fly at a new speed of 1.26[tex]v_{0}[/tex].
As, P = F v
So, P = kv³
Then, v/v0 = [tex]\sqrt[3]{P/P0}[/tex].
Therefore, after substituting the values, the speed will be 1.26[tex]v_{0}[/tex].
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A beam of electrons moves at velocity 4.6 ⋅105 m/s in the positive x direction through a uniform 2.8 T magnetic field pointing in the positive y direction. What direction does the magnetic force point? +x -x +y -y +z -z What is the magnitude of the force? F
Answer:
The magnetic force on a moving charged particle is given by the Lorentz force law, which states that the force is equal to the product of the particle's charge, its velocity, and the magnetic field. Since the magnetic field points in the positive y direction and the velocity of the electrons is in the positive x direction, the magnetic force on the electrons will point in the negative z direction (assuming we are using the right-hand rule to determine the direction of the force). The magnitude of the force can be found using the formula above: F = q * v * B, where q is the charge on the electrons, v is their velocity, and B is the strength of the magnetic field. The charge on an electron is -1.6 x 10^-19 C, so the magnitude of the force on the electrons will be: F = (-1.6 x 10^-19 C) * (4.6 x 105 m/s) * (2.8 T) = -2.19 x 10^-13 N.
list the 8 types of waves found on the electromagnetic spectrum from longest to shortest wavelength.
The 8 types of waves found on the electromagnetic spectrum, from longest to shortest wavelength, are: Radio waves , Microwaves , Infrared radiation, Visible light, Ultraviolet radiation, X-rays, Gamma rays.
The electromagnetic spectrum is a range of electromagnetic waves that includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.
The wavelength of an electromagnetic wave is the distance between consecutive points of equal phase in the wave. The shorter the wavelength, the higher the frequency of the wave.
Radio waves have the longest wavelength and the lowest frequency of the electromagnetic waves. Gamma rays have the shortest wavelength and the highest frequency.
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at one particular moment, a 17.0 kg toboggan is moving over a horizontal surface of snow at 4.40 m/s. after 6.75 s have elapsed, the toboggan stops. use a momentum approach to find the magnitude of the average friction force (in n) acting on the toboggan while it was moving.
The magnitude of the provided average friction force F (in n) which is acting on the toboggan during it was moving is 8.66 N
What is a toboggan in the USA?Toboggan is a long flat-bottomed light sled composed usually of thin boards curved up at one end with usually low handrails at the sides. : a downward course as well as a sharp decline.
Solution:Given:
vi = 4.1 m/s
vf = 0
Δv = v final - v initial
= 0 - 4.1 = -4.1 m/s
Δ momentum i.e mΔv = (19 kg).(-4.1 m/s)
= 77.9 kgm/s
The average friction force (Ff) takes 9 seconds to take the toboggan to a end point, hence, impulse = Ft
= Ff(9)
Impulse is = Δ momentum, so
Ff(9) = 77.9;
Ff = 8.66 N
Is a beanie and a toboggan the same thing or not ?Touque, Toque and Tuque is in fact the same wool which has a Beanie with three distinct spellings. And at last but not at least in the southern American states , Toboggan is the name used for a wool knitted hat that is worn during the colder months of the year.To know more about toboggan visit
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Describe what the motion of the rigid system will be if:
a. The first condition for equilibrium is not satisfied.
b. The second condition for equilibrium is not satisfied.
c. Neither condition for equilibrium is satisfied.
The motion of the rigid system will be (a) linear (b) rotational (c) both linear and rotational
The first condition for equilibrium states that the body must have a net force of zero. This means that when the net force acting on a body is not zero the body will continue to move in a straight path and the motion of the rigid body will be linear.
The second condition for equilibrium states that the body must have zero net torque acting on the body for achieving equilibrium. torque is the rotational equivalent of force. Therefore, when the net torque is not zero, the rigid body keeps rotating which leads to a rotational motion.
When both the conditions of equilibrium are not satisfied the rigid body does not achieve the static equilibrium.
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Which of the following is a real piece of evidence (from the New Horizons mission) pointing to recent or ongoing geological activity on Pluto?
One piece of evidence from the New Horizons mission that suggests recent or ongoing geological activity on Pluto is the presence of mountains with smooth, sediment-like material on their surfaces.
This material is thought to be composed of water ice that has been altered by geologic processes, such as the flow of glaciers or the collapse of underground caverns.
Other evidence of recent or ongoing geological activity on Pluto includes the presence of ridges, valleys, and other landforms that suggest the existence of tectonic activity, as well as the existence of ice on the surface that has a relatively high surface temperature, indicating that they may have recently been exposed to heat.
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In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 35.5 m, and the heights of the Jackson and Walton buildings are, respectively, 15.5 m and 22.5 m. Ignore air resistance.
(a) The first balloon launched by the Jackson team hits Walton dorm 2.2 s after launch, striking it halfway between the ground floor and the roof. Find the direction of the balloon's initial velocity. Give your answer as an angle measured above the horizontal.
(b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.
The basic kinematic equations for horizontal and vertical motion are as follows:
s = v₀t + ¹/₂at²
Horizontal motion is:
x = v₀ₓt + ¹/₂aₓt²
x = v₀ₓt
x = v₀ cosαt
Because there is no air resistance: x = v₀ cosθt
Vertical motion is:
y = v₀[tex]__y[/tex]t + ¹/₂a[tex]__y[/tex]t²
y = v₀ sinαt - ¹/₂gt²
Solve both for the velocity trigonometric function term as follows:
y = v₀ sinαt - ¹/₂gt²
v₀sinαt = ¹/₂gt² + y
v₀sinα = ¹/₂gt² + y/t
and
x = v₀ cosαt
v₀cosα = x/t
Now divide these two equations and we get
v₀sinα/v₀cosα = tanα [tex]=\frac{1/2gt + \frac{y}{t} }{\frac{x}{t} }[/tex]
tan α [tex]= \frac{1/2gt + \frac{y}{t} }{\frac{x}{t} } = \frac{gt^2}{2x} + \frac{y}{x}[/tex]
tan α [tex]= \frac{gt^2}{2x} + \frac{y}{x}[/tex]
Enter a value, x is the distance between the boarding 35.5 m, and y is the difference between the launch height and the drop point. The launch height is 15.5 m and the landing height is 11.0 m, so y = -4.5 m. Finally, we are told the projectile travel time is 2.2 s.
tan α [tex]= \frac{gt^2}{2x} + \frac{y}{x}[/tex]
tan α [tex]= \frac{(9.8)(2.2)^2}{2(35.5)} + \frac{-4.5}{35.5}[/tex]
tan α [tex]= 0.668 - 0.126[/tex]
tan α [tex]= 0.542[/tex]
α = tan⁻¹ 0.542
α = 28.4°
For the second launch, y₂ is +7.0 m launch altitude is still 15.5 m, but the deployment altitude is now 22.5 m, and x is still 35.5 m. The angle remains 28.4°. This time we don't know the flight time or initial velocity we are asked to find. Using horizontal distances, we can solve for time.
x = v₀.cosα.t
t² = x/v₀.cosα
Now do it for y₂:
y₂ [tex]= v_0sin(\alpha) t - 1/2gt^2[/tex]
y₂ [tex]= v_0sin(\alpha) (\frac{x}{v_0cos(\alpha)} ) - 1/2g (\frac{x}{v_0cos(\alpha)} )^2[/tex]
y₂ [tex]= x tan (\alpha ) - \frac{gx^2}{2v_0cos(\alpha)^2}[/tex]
[tex]\frac{gx^2}{2v_0cos(\alpha)^2} = x tan (\alpha ) - y_2[/tex]
We need to solve v₀:
[tex]\frac{gx^2}{2v_0cos(\alpha)^2} =\frac{1}{ x tan (\alpha ) - y_2}[/tex]
2v₀cos (α)² [tex]= \frac{gx}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{1}{2cos(\alpha)^2} ) \frac{gx}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{x^2}{cos(\alpha)^2} ) \frac{g/2}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{x}{cos(\alpha)^2} ) \sqrt{ \frac{g/2}{ x tan (\alpha ) - y_2}}[/tex]
Now we can enter values:
v₀² [tex]= (\frac{x}{cos(\alpha)^2} ) \sqrt{ \frac{g/2}{ x tan (\alpha ) - y_2}}[/tex]
v₀² [tex]= (\frac{35.5}{cos(28.4^0)} ) \sqrt{ \frac{9.8/2}{ 35.5 tan (28.4^0) - 7.0}}[/tex]
v₀² = 40.386 [tex]\sqrt{\frac{4.9}{12.17} }[/tex]
v₀² = 40.386 (0.634)
v₀² = 25.62 m/s
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i need help creating a realistic planet with the following information
Only the Sun and the Moon are brighter than the planet Venus, which represents the goddess' own beauty and makes for a lovely spectacle in the sky.
What planet in solar system considered as goddesses?The ancient Greeks gave the name Athena—after their goddess of wisdom—to the fourth planet from the Sun.
The same planet was given the name Minerva by the Romans, who did so in honor of Athena in Greek mythology. The first manned spacecraft to visit the planet was given the name Athena by the Americans.
Therefore, In honor of their goddess of love and beauty, the Romans gave the brightest planet, Venus, that name. After the telescope was created in the early 1600s, the planets Uranus and Neptune were also found.
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A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 10.0 s. We have taken counterclockwise rotation to be positive.How long is the time interval during which the speed of the wheel is increasing?
The time interval during which the speed of the wheel is increasing is 4 s.
What is angular acceleration?The temporal rate at which angular velocity changes is known as angular acceleration. The standard unit of measurement is radians per square second.
The angular velocity at time t = 0, is ω₁ = - 6.00 rad/s.
The angular velocity at time t = 10.0 s, is ω₂ = +4.00 rad/s.
Angular acceleration of the wheel = change in angular velocity /time interval
= ( 4.00 - (-6.00))/10 rad/s²
= 1.0 rad/s²
Hence, angular velocity becomes zero at time = ( 0 - ( -6))/1.0 s = 6 s.
So, during t = 0 to t = 6s, the clockwise angular velocity of the wheel decreases from 6.00 rad/s to 0.00 rad/s and during t = 6s to t = 10s , the counterclockwise angular velocity of the wheel increases from 0.00 rad/s to +4.00 rad/s.
Hence, the time interval during which the speed of the wheel is increasing is = 10 s - 6 s = 4 s.
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EXPLAIN THE MEASUREMENT PRINCIPLE OF ATOMIC SPECTROMETERS
Atomic absorption spectroscopy, often known as AAS or AA spectroscopy, is one of the earliest methods for elemental analysis to be established for the market.
What is Atomic Spectrometer?The analytical method known as flame atomic absorption spectroscopy (Flame AAS or FAAS) was first commercially released in the 1960s after being invented in 1952.
The method has been well-liked ever since for its dependability and simplicity. AAS is an analytical method for figuring out how much of a particular element is in a sample. It is based on the idea that atoms (and ions) may absorb light with a certain, distinct wavelength.
The atom absorbs the energy (light) when it is present at this particular wavelength. By absorbing energy (light) at a certain wavelength, an electron is stimulated from the ground state to a higher energy level.
Therefore, Atomic absorption spectroscopy, often known as AAS or AA spectroscopy, is one of the earliest methods for elemental analysis to be established for the market.
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Three particles having charges of equal magnitude q are fixed at the conrners of an equilateral triangle as shown. two of the charges are negative: the other is positive. which of the following vectors best represents the direction of the resultant electric field at point p, the center of the triangle?
Vector B of the following vectors best represents the direction of the resultant electric field at point p, the center of the triangle.
What is vector?A quantity or phenomenon that has two independent properties i.e magnitude and direction is named as vector.
At the middle, where it is zero, one can see that the three charges each produce cancelling fields thanks to symmetry.In addition to the triangle's center, the second panel of the picture shows three additional sites in the middle of each triangle leg where E=0, however they are more challenging to calculate analytically.Adding the electric field vectors resulting from each of the two lower point charges will yield the electric field at point P.
E = E1+ E2.
According to the bottom panel of the picture, a point charge's electric field has the formula E = kr2qr.
E =k ea2q uphill and to the right at 60, and E2 =kea2q upward and to the left at 60.
Therefore, E= E1 + E2 = kea2q[(cos60i+sin60j) + (cos60i+sin60j)] = kea2q[2(sin60j)
= 1.73kea2qj. i.e vector B
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Which formula gives the displacement of a ball At seconds after it is thrown vertically upward (positive
direction) at an initial velocity, vi
Answer:
Δy = viy t + (1/2)gt^2
Explanation:
[tex]y = y_{i}+v_{iy}_t + (1/2)a_{y}t^{2}[/tex]
Δy = viy t + (1/2)gt^2
A square meter of the axon membrane has a resistance of 0.2 ohms. The membrane is 7.5 x 10‐⁹ m thick. What is the resistivity of the membrane?
Answer:
using the formula
Resistance=Resistivity × length/area
Area=1 ,Resistance(R)=0.2ohm ,resistivity(P)=? ,length=7.5×10^-9
R=Pl/A
Pl=RA
P=RA/l
P=0.2×1/7.5×10^-9
P=0.027×10^9
P=2.7×10^7ohmsmeter
The resistivity of the membrane is 2.7×10⁷ ohm-meter.
What is resistivity?
Electrical resistance of a conductor with a unit cross-sectional area and unit length is called resistivity. Resistivity is a distinctive attribute of any material that may be used to compare different materials based on how well they conduct electric currents. Low conductivity is indicated by high resistance.
Mathematically the relation between resistance and resistivity can be written as:
Resistance=Resistivity × length/area
Given parameters:
Area of the membrane: A=1 m²
Resistance(R)=0.2ohm ,
resistivity(ρ)=?
length=7.5×10^-9 m.
Now:
R=ρl/A
⇒ρl=RA
⇒ρ=RA/l
⇒ρ=0.2×1/7.5×10⁻⁹
⇒ρ=0.027×10⁹
⇒ρ=2.7×10⁷ ohm-meter.
Hence, the resistivity of the membrane is 2.7×10⁷ ohm-meter.
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A student is trying to determine the muzzle
velocity (initial) of a bullet that is too fast to
measure directly. The student fires the 0.05kg
bullet into a 4kg block of wood initially at rest.
After the collision, the block, with the bullet
embedded inside moves to the right with a
speed of 1.87m/s right.
before collision:
Pbullet
Pblock
after collision:
Pcombined
kg m/s
kg m/s
kg m/s
How fast was the bullet fired?
m/s
mu + MU = (m + M) V... eq (1)
given:
m=0.05 kg, M=3.5 kg, U= 0 and V=1.82 m/s.
put these numbers to equation (1)
0.05×u +0 =(0.05+3.5)×1.82
u=3.55×1.82 /0.05
u= 6.461/0.05
u=129.22m/s ...(2)
prior to a collision
Bullet: |p|bullet =mu =0.05129.22=6.461 kg/s
|p | block = MU=3.5×0 =0 kg.m/s
After collision
Combining, |p| equals (m+M)V = (0.05+3.5) 1.82 =6.461 kg.m/s.
Equation (2) shows the initial speed of the projectile.
=129.22 m/s.
what is collision?
Collision is defined as the meeting of two or more things with such force that both or all of them suffer harm or have their development significantly slowed.
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Cynthia's broker charges her a commission of $88 for every $1000 of stock bought or sold. Cynthia bought
2,000 shares of Ombor Medical Supplies at $35.49 apiece. As the price rose and fell, she sold off part of her
holdings. When the price rose to $48.57, she sold 600 shares. The price fell somewhat to $46.10, so she sold
1,150 of her shares. When the price climbed to $53.46, she sold off the remainder of her holdings. How much
profit did Cynthia make in total?
a. $9,889.82
b.
$24.542.00
c. $16,312.06
d. $74,799.58
Please select the best answer from the choices provided
$9,889.82 much profit did Cynthia make in total.
What is Stock?In the financial markets, it can be difficult to tell stocks from shares. Both terms are typically interchangeable in American English when referring to financial equities, more precisely, securities that signify ownership in a public corporation.
The more inclusive, generic term is "stocks." It is frequently used to refer to a portion of ownership in one or more businesses.
In comparison, "shares" has a more precise connotation in everyday speech: It frequently refers to the ownership of a specific business.
Therefore, $9,889.82 much profit did Cynthia make in total.
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the sun goes down, and over all these barren reaches by the tide such unelusive glories fall, i almost dream they yet will bide 5until the coming of the tide
The passage is describing the beauty of Acadie, a place that is home to the speaker. This passage is from Bliss Carman's "LOW TIDES" .
The sun is setting, and the speaker is captivated by the beauty of the landscape, which is enhanced by the unelusive glories of the tide. The speaker also reflects on a beloved face being gone for a long time and is moved by a grievous stream, which meanders through the fields of Acadie as if it is trying to figure out why the beloved face is gone. The speaker almost dreams that the beauty of the place will remain until the beloved face returns. The passage conveys a sense of longing and hope for the beloved to come back to Acadie.
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What is observation of demonstrating the force of attraction and repulsion between two current parallel carrying conductor
Answer:
The force of attraction and repulsion between two current-carrying parallel conductors can be demonstrated using a simple experiment. To do this, you will need two long, straight conductors, a power source, and a means of measuring the force between the conductors.
First, connect the two conductors to the power source so that they are carrying current in the same direction. Place the conductors parallel to each other, and measure the force between them using a spring scale or other device. You should observe a force of attraction between the conductors.
Next, reverse the direction of the current in one of the conductors, and measure the force between the conductors again. This time, you should observe a force of repulsion between the conductors.
This experiment demonstrates that current-carrying conductors exert a force of attraction on each other when the currents are in the same direction, and a force of repulsion when the currents are in opposite directions. This phenomenon is known as the Lorentz force.
Every winter morning when the sun is shining bright, a man living in Montana pulls back the drapes on a large, south-facing window. In this way, he helps heat his home using ________.
a. passive solar
b. active solar
c. photovoltaic
d. conductive solar
e. radioactive solar
Answer:
(b) active solar because the solar radiation passing thru the window will help to heat his room
Please answer both questions!!
1. Apply Concepts What is inertia? Use an
example in your description.
2. Integrate Information What is the
difference between balanced forces and
action-reaction forces?
Answer:
1. Inertia is the property of an object that resists changes in its state of motion. An object with more mass has more inertia, meaning it is harder to change its motion. For example, a heavy truck has more inertia than a small car, so it takes more force to get the truck moving or to change its direction of motion.
2. Balanced forces are forces that act on an object in opposite directions and are equal in magnitude, resulting in no net force on the object. This means that the object will not accelerate or change its state of motion. Action-reaction forces, also known as Newton's Third Law forces, are forces that act on two objects in response to each other. These forces are always equal in magnitude and opposite in direction, but they do not cancel each other out because they act on different objects. An example of action-reaction forces is the force of a person pushing against the ground and the force of the ground pushing back against the person. While these forces are equal and opposite, they do not cancel out because they act on different objects.
What is meant by the projectile height?
Answer:
Explanation:
The object's height is the vertical position along its trajectory.
Xiao,a 7-year-old Chinese child,and Jess,a 7-year-old American child,are each listening to an audio tape in their individual rooms.At one point,the audio on both tapes gets covered by static.
Xiao speculates that the unheard portion refers to a verb, whereas Jess speculates that it relates to a noun.
What does the term "audio" mean?Anything related to sound in terms of receiving, transmitting, reproducing, or its particular frequency is referred to as audio. A stereo is an illustration of an audio object. YourDictionary.
Do physical audio speakers work well?Audio Physical loudspeakers enjoy a solid reputation among music enthusiasts and are renowned for both their performance and high-quality design. Throughout the more than 30 years of the marque, this history of quality has persisted despite some more difficult times.
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A 42.4 N block is sliding down an inclined plane with a constant speed. The kinetic friction acting on the block is N.
When a mass m particle is released onto a smooth inclined plane (where the frictional force F=0), it will glide down the slope.
We resolve in the direction of motion in order to get the particle's sliding acceleration.
F=ma,
mg cos(90∘−θ)=ma,
g cos(90∘−θ)=a,
g sin(θ)=a.
How many Newtons is the net force while the block is travelling at a constant speed?
Zero. Newton's first law of motion states that any object travelling at a constant speed experiences no net external forces, hence the total amount of forces acting on the object must be zero. The mathematical expression for an item being under no net external force is Fnet=0 or F=0.
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A rectangular copper strip is 20 cm long, 0.1 cm wide and 0.4 cm thick. Determine the resistance between (i) opposite ends (ii) opposite sides. The resistivity of copper is 1.7 × 10–6 Ω cm
The resistance at opposite ends is 8.4 × 10–6 Ω cm. The resistance at opposite sides is 0.021 × 10–6 Ω cm.
What is Resistance?The obstruction to current flow in an electrical circuit is measured by resistance. The Greek letter omega represents the unit of measurement for resistance, known as ohms.
Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance. Ohm's Law is attributed to him as its creator.
In the given question, The length of the strip = 20 cm, The breadth of the strip = 01. and The thickness of the strip= 0.4 The resistivity of the copper= 1.7 × 10–6 Ω cm.
Therefore, The resistance at opposite ends is 8.4 × 10–6 Ω cm. The resistance at opposite sides is 0.021 × 10–6 Ω cm.
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the vertical and horizantal distance of the progetile will be equal if angel of progectile is
Answer:
The vertical and horizontal distance of a projectile will be equal if the angle of projection is 45 degrees.
Explanation:
This is because at an angle of 45 degrees, the projectile will be equally influenced by the horizontal and vertical components of its motion. As a result, the projectile will travel the same distance horizontally as it does vertically.
For other angles of projection, the projectile will be more influenced by either the horizontal or the vertical component of its motion, depending on the angle.
At an angle of 90 degrees (straight up), the projectile will be primarily influenced by the vertical component of its motion, while at an angle of 0 degrees (horizontal), the projectile will be primarily influenced by the horizontal component of its motion.
A(n) 0.298 kg soccer ball approaches a player horizontally with a speed of 15 m/s. The player illegally strikes the ball with her hand and causes it to move in the opposite direction with a speed of 17 m/s..
What is the magnitude of the impulse de- livered to the ball by the player? Answer in units of kg m/s.
The magnitude of the impulse delivered to the ball by the player is -9.536 kg-m/s
How do you calculate the magnitude of the impulse delivered by the player?Given that,
Mass of a soccer ball, m = 0.298 kg
Initial speed, u = 15 m/s
Final speed, v = -17 m/s (negative as it is in opposite direction)
(a) Impulse = change in momentum
J = 0.298 × (-17 -15)
J = -9.536 kg-m/s
Therefore the magnitude of the impulse delivered to the ball by the player is -9.536 kg-m/s.
What is the formula for the impulse's magnitude?The object's change in momentum is equal to the impulse it experiences. The formula for magnitude of impulse is F • t = m • v. When two objects collide, an impulse occurs, which both causes and equals the change in momentum.
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explain the difference between a ligand-gated k channel and a voltage-gated k channel. match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer. resethelp 1. the ligand-gated channel opens or closes in response to blank .target 1 of 2 2. the voltage-gated channel opens or closes in response to blank .
The voltage-gated ion channels allows permeation of only one type of ion whereas, ligand-gated channels are less selective and allows permeation of two or more types of ions via the channel pore.
What is the difference between ligand-gated and voltage gated K channels?Ligand-gated ion channels are integral membrane proteins that contain a pore which allows regulated flow of selected ions across plasma membrane. Voltage-gated potassium channels are transmembrane channels specific for potassium and are sensitive to voltage changes in the membrane potential of cell .
1. Ligand-gated channel opens or closes in response to blank the binding of a ligand.
2. Voltage-gated channel opens or closes in response to differences in membrane potential.
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A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet/sec. How fast is the top of the ladder moving down the wall when the base of the ladder is 7, 15, and 24 feet from the wall?
The velocity of the ladder when the base of the ladder is 7, 15, and 24 feet from the wall is -0.875, -2.25, and -10.286 respectively.
Given, the length of the ladder= 25 ft
Let x be the distance between the wall and the ladder and h be the height of the ladder from the ground
x² + h² = (25)²
x² +h²= 625
h²= 625- x²
h= [tex](625- x^{2})^{1/2}[/tex]
[tex]\frac{dh}{dx}[/tex] = [tex]\frac{1}{2}[/tex] [tex](625- x^2)^{-1/2} * (-2x)[/tex]
[tex]\frac{dh}{dx}[/tex] = [tex]\frac{-x}{\sqrt{ (625-x^2)}}[/tex]
We have dx/dt= 3 ft/sec
Therefore, by applying the chain rule, we can get the value of dh/dt as:
dh/dt= dh/dx *dx/dt
=[tex]\frac{-x}{\sqrt{ (625-x^2)}}*3[/tex]
=[tex]\frac{-3x}{\sqrt{ (625-x^2)}}[/tex]
Now substituting the different values of x in the acquired equation
When x= 7, dh/dt= [tex]\frac{-7}{8}[/tex] ft/sec= -0.875 ft/sec
When x= 15, dh/dt= [tex]\frac{-9}{4}[/tex] ft/sec= -2.25 ft/sec
When x= 24, dh/dt= [tex]\frac{72}{7}[/tex] ft/sec= -10.286 ft/sec
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alex thinks 131 degrees are neat. what is the maximum number of interior angles of a convex n-gon that can measure 131 degrees?
A polygon whose internal angles are all less than 180 degrees is referred to as a convex n-gon. The same can be computed as:
The formula (n-2) × 180 degrees, where n is the number of sides in the polygon, gives the sum of the measures of the interior angles of a convex n-gon.
The total of the measures of the remaining (n-x) angles must equal (n-2) × 180 - 131x degrees if x is the number of internal angles of the n-gon that measure 131 degrees. Since the internal angles of a convex n-gon must have measures that are less than 180 degrees,
this implies that
(n-2)180 - 131x < (n-x)180
Solving this inequality for x,
we find that
[tex]x < \frac{(n-2)}{3}[/tex]
Therefore, the maximum number of interior angles of a convex n-gon that can measure 131 degrees is (n-2)/3.
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A mass on a spring undergoes SHM. When the mass is at its maximum displacement from equilibrium, its instantaneous velocity A) is zero. B) is less than maximum, but not zero. C) is maximum D) cannot be determined without mass information given. E) cannot be determined without spring constant information given.
When the mass is at its maximum displacement from equilibrium, the instantaneous velocity 'is zero'.
What is velocity?
A measure of a moving object's speed and direction is called velocity. It can be expressed as a vector quantity with direction and magnitude (speed).
According to the given question:
An object has exhausted all of its potential energy to move when it reaches its maximum displacement from equilibrium. Consequently, the object has zero instantaneous velocity because it lacks momentum to continue moving.
Hence, Option A is correct.
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A roller coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller
coaster shown in Fig. P7.62 has a circular loop of radius R in the vertical plane. (a) First, suppose the car barely makes it around the
loop; at the top of the loop the riders are upside down and feel weightless. Find the required height of the release point above the bottom
of the loop, in terms of R. (b) Now assume that the release point is at or above the minimum required height. Show that the normal force
on the car at the bottom of the loop exceeds the normal force at the top by six times the weight of the car. The normal force on each rider
follows the same rule. Such a large normal force is dangerous and very uncomfortable for the riders. Roller coasters are therefore not
build with circular loops in vertical planes. Figure P5.24 and the photograph on page 134 show two actual designs.
a) Height is calculated as = 5R/2 b) It is shown that the normal force on the car at the bottom of the loop exceeds the normal force at the top by six times the weight of the car.
What is meant by normal force?The force that surfaces exert to prevent solid objects from passing through each other is known as the normal force .
a) At point A, PE = m g h
At point B, PE = 1/2 * m * (vB)²
At point C, PE = m(vC)²/R - mg
m is mass vB is velocity at B
vC= √mgR/m = √gR
For conservation of energy at point C and B
1/2 * m * (vB)² + 1/2 * m * (vC)² + mg (2R) ( height of c = 2R)
(vB)² = gR + 2(2gR)
So, vB = √5gR
Conservation of energy between point A and B,
1/2 * m * (vB)² = mgh
Height, h = 5R/2
b) Normal force at topmost point C is
= m(vC)²/R - mg
Normal force at bottom point B is
= mg + m (vB)²/R
NB = mg + m(5gR)/R
= 6 mg
Therefore, we can say that NB > NC
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A box of mass m slides up a ramp with initial velocity +0. The kinetic friction force on the box has magnitude f. Which of the following is a correct equation that could be used to determine the acceleration a of the box? (A) -f=ma (B) mg sin 0 - - F=ma (C) f-mg sino 0 = ma
(D) -f-mg sino 0 = ma
The equation that could be used to determine the acceleration a of the box is (-f-mg sin 0 = ma)
What is kinetic friction force on inclined plane?If the direction of motion of the mass is up the plane, then the frictional force F will act down the plane.
Normal force N is exerted on the body by the plane due to the force of gravity i.e. mg cos θ. These two will be equal hence cancelled out.
Here, according to the question,
Box is moving up so, Force of friction is acting downwards and mg sin 0 is also acting downwards. Both are acting against the motion of the box so both terms will be negative i.e. (-f) and (-mg sin 0)
We know resultant force is equal to (ma)
So, (-f) + (-mg sin0) = ma
-f - mg sin0 = ma
The equation that could be used to determine the acceleration a of the box is (-f-mg sin 0 = ma)
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