The launch velocity of the projectile is 13.28 m/s.
What is projectile motion?
The motion of an object thrown in the air under the force of gravity is known as projectile motion.
Since the object is launched horizontally, its initial velocity along the vertical direction is zero. From the second kinematic equation,
s=u*t+(1/2)at^2.
where s is the displacement, t is the time, u is the initial velocity and a is the acceleration. Since the height is decreasing, so it will be taken negative.
For the vertical motion, s=-19.3 m, a=-9.8 m/s^2 and u=0. Put the values in the above equation and solve it.
-19.3 = (0)*t+(1/2)*(-9.8)*t^2
19.3 = (1/2)*(9.8)*t^2
t=1.98 s
Since the velocity along the horizontal direction is constant, the displacement along the horizontal direction is given by the formula,
X=vt
where X is the horizontal displacement, v is the initial horizontal velocity and t is the time.
For the horizontal motion, X=26.3 m and t=1.98 s. Put the values in this equation and solve it.
26.3=v*(1.98)
v=13.28 m/s
The launch velocity is equal to the initial horizontal velocity, so it is equal to 13.28 m/s.
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The audible frequency range for a person is 30HZ to 16500HZ. Determine the largest wavelength of sound in air the person can detect (speed=340m/s)
Answer:
We have the formula,
V=λ×v
where,
V is the velocity of sound =330ms
−1
v is the frequency
λ is the wavelength
We have a range of frequencies from 20Hz to 20,000Hz
Hence for frequency v=20Hz, we have
330=20×λ
Therefore, λ=
20
330
m
Explanation:
Sammy Speedy, a 69.5 kg jogger, takes a jog along a walk path. If Sammy expends 1,750.0 J while jogging, how fast is he moving?
The speed of Sammy, given that he expends 1750 J while jogging is 7.1 m/s
Data obtained from the questionMass (m) = 69.5 KgEnergy (E) = 1750 J Speed (v) =?How to determine the speedThe speed of Samnmy can be obtained as illustrated below:
E = ½mv²
1750 = ½ × 69.5 × v²
1750 = 34.75 × v²
Divide both side by 34.75
v² = 1750 / 34.75
Take the square root of both side
v = √(1750 / 34.75)
v = 7.1 m/s
Thus, Sammy is moving with a speed of 7.1 m/s
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A 31.4-kg wheel with radius 1.21 m is rotating at 283 rev/min. It must be brought to a stop in 14.8 s. Find the required average power. Assume the wheel to be a thin hoop.
The average power required to stop the wheel is 2795 Joule.
To find the answer, we need to know about the linear velocity, acceleration and force on the wheel.
What is the angular frequency of the rotating wheel?Mathematically, angular frequency= 2×π×frequencySo, angular frequency= 2×π× 283 rev/min= 2×π×(283/60) rev/s
= 30 rad/s
What's the expression of velocity from angular frequency?Mathematically, angular frequency= velocity/radiusSo, velocity= angular frequency × radius Here, radius of the wheel= 1.21mSo, velocity= 30×1.21 m = 36.3 m/s
What will be the acceleration of the wheel, if the final velocity is zero, initial velocity 36.3m/s and time is 14.8 s?Mathematically, acceleration= changeing velocity/timeHere, changing velocity= 36.3m/s and time = 14.8 sSo, acceleration= 36.3/14.8 = 2.45 m/s²What's the force experienced by the wheel?The force on the wheel= mass× acceleration
= 31.4 × 2.45 = 77 N
What's the average power of the wheel?Mathematically, power= work done / time = force×velocityPower= 77 × 36.3 = 2795 J.Thus, we can conclude that the average power of the wheel is 2795 J.
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A 50 mW laser beam is polarized horizontally. It then passes through two polarizers. The axis of the first polarizer is oriented at 30 degrees from the horizontal, and that os the second is oriented at 60 degrees from the horizontal. What is the power of the transmitted beam
The power of the transmitted beam is 28.1*10^-3.
The wireless strength consortium turned into installed in 2008 to expand interoperable standards across producers. Its Qi inductive power standard published in August 2009 enables high-performance charging and powering of portable gadgets of up to five watts over distances of four cm (1.6 inches).
Electricity transmission is the motion of power from its region of technology to a region wherein it is implemented to perform beneficial paintings. Power is defined officially as units of electricity consistent with units of time.
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The ________-year solar cycle is characterized by a variation in the number of sunspots and a reversal of the polarity of the Sun as a whole.
22 year solar cycle is characterized by a variation in the number of sunspots and a reversal of the polarity of the Sun as a whole.
What are sunspots?
Sunspots are caused by disturbances in the Sun's magnetic field welling up to the Sun's visible surface.
Sunspot are region of the earth that are more darker than other surfaces. They have a reduced temperature.
If sunspots are active, more solar flares will result creating an increase in geomagnetic storm activity for Earth.
Here, the sun's magnetic field changes polarity approximately every 11 years. So, for reversal polarity of the sun, 22 year solar cycle is characterized by a variation in the number of sunspots and a reversal of the polarity of the Sun as a whole.
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Two concentric, coplanar, circular loops of wire of different diameter carry currents in the same direction. Describe the nature of the force exerted on the inner loop by the outer loop and on the outer loop by the inner loop.
Answer:
Both will be attractive in nature.
Explanation:
In the given case, the direction of the magnetic field is same in both loops as the direction of the current is same in both loops. When two parallel straight wire carrying current in the same direction are brought close to each other, the force between them is attractive in nature. In the same way, when two coplanar, circular and concentric loops of wire are carrying current in the same direction, the force between them is attractive in nature. It can be checked by using right hand thumb rule.
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A book placed on a table does not move identify the forces in action and identify why the book foes not move
Answer:
See below
Explanation:
There is the normal force of the book on the table.....the table exerts the same force ( upwards) on the book.
All of the forces result in a net zero force on the book so it does not move (there are no horizontal forces on the book)
why new zealand and sydney celebrate the new year hours before it is celebrated in india.
Due to geographical location of new zealand and sydney, they celebrate the new year hours before it is celebrated in india.
Why new zealand and sydney celebrate the new year hours before it is celebrated in india?New Zealand and Sydney celebrate the new year hours before it is celebrated in india because of its geographical position close to the International Date Line. New Zealand is considered one of the first countries in the world that welcome the New Year.
So we can conclude that due to geographical location of new zealand and sydney, they celebrate the new year hours before it is celebrated in india.
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A 110-kg horizontal beam is supported at each end. A 320-kg piano rests a quarter of the way from one end. What is the vertical force on each of the supports
Vertical force on left support = 2891 N
Vertical force on right support = 1323 N
Let's assume the Length of the horizontal beam = L(see diagram)
Mass of beam (m) = 110kg
Mass of piano(M) = 320kg
Weight of the Horizontal beam(W1) =mg = 110×9.8= 1078N
Net force acting on the beam =0
[tex]F_{L}[/tex] - Mg - mg + [tex]F_{R}[/tex] = 0
[tex]F_{L}[/tex] = Force support to the left
[tex]F_{R}[/tex] = Force support to the right
τ = F×r where, τ= Torque
Net torque is also 0
[tex]F_{R}[/tex]L - Mg[tex]\frac{L}{4}[/tex] - mg[tex]\frac{L}{2}[/tex] =0
[tex]F_{R}[/tex] = ([tex]\frac{M}{4} + \frac{m}{2}[/tex])g = 1323 N
[tex]F_{L}[/tex] = (M + m)g - [tex]F_{R}[/tex] = 2891 N
Hence Vertical force on left support is 2891 N and on right support is 1323 N
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When a planet temporarily moves westward in the sky over the course of several weeks or months (instead of eastward, as it typically does), we call it:
When a planet temporarily moves westward in the sky over the course of several weeks or months (instead of eastward, as it typically does), we call it retrograde motion.
In astronomy, retrograde motion refers to a body's actual or apparent motion in the opposite direction from the majority of solar system objects or other astronomical systems having a favored direction of motion.
Planets usually appear to migrate eastward when compared to the fixed stars.
However, on occasion, they appear to briefly stall in their eastward travel and then migrate westward (backward) in front of the stars for a few months.
They then pause once again. They resume their eastward movement after that.
This motion is known as retrograde motion and sometimes it is just an illusion.
Hence, when a planet temporarily moves westward in the sky over the course of several weeks or months (instead of eastward, as it typically does), we call it retrograde motion.
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How can we change direction of light? Name this phenomenon. any indian didis and bhayas to help (ik i said australian any will work for me)goys please help im in grade 6 and my teacher didnt give us the answer to a question in notebook:(
why does the production of electricity by friction always yield equal amounts of positive and negative charge
Friction yields equal amounts of positive and negative charge as positive and negative charges occur in pairs.
What is frictional electricity:
When two charged particles are rubbed together, transfer of charge takes place. This leads to production of electricity, as one object loses electrons and gains positive charge while the other object gains electrons and becomes negatively charged.
All objects contain equal amounts of positive and negative charge. Thus, when friction is caused between them, it yields equal amounts of positive and negative charge which is known as static electricity.
One of the prime example of static electricity is rubbing silk cloth over glass rod. Here, the glass rod loses electrons while silk gains electrons. thus, the glass rod becomes positively charged and silk becomes negatively charged.
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A sky diver, mass 90 kg, reaches a terminal velocity of 60 m/s. What is the approximate magnitude of the force of air resistance?.
Answer:
The approximate magnitude of the force of air resistance is 540 N.
Explanation:
How does the meaning of the word isometric relate to determining if an isometric transformation occurred?.
In an isometric transformation, the shape does not change size.
What is isometric transformation?A shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.
A stiff transformation called an isometry keeps perimeter and area constant while preserving length and angle measurements.
As a result, while dilations are not isometric since the image and preimage are comparable figures rather than congruent figures, translations, reflections, and rotations are.
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Which part of the heating curve corresponds with the boiling of liquid water?
Ο Α. Α
OB. B
O C. D
OD. C
Answer:
The answer is B
Explanation:
The section C of the heating curve represents the liquid phase, which is where liquid water is heated. Hence option D is correct.
What is heating?The body or particle is considered to be heating up as the temperature rises.
100°C is the boiling point of water at 1 atm of pressure.
The term "enthalpy of vaporisation" refers to the amount of heat energy needed to change liquid water into steam.
Enthalpy of vaporisation has a greater value than enthalpy of fusion.
The amount of power needed to melt ice into liquid water is known as the enthalpy of fusion.
As a result, section C illustrates the heating of liquid water.
Hence option D is correct.
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If 710- nm and 660- nm light passes through two slits 0.65 mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.5 m away
0.23 mm far apart are the second-order fringes for these two wavelengths on a screen 1.5 m away.
Given wavelengths 710nm and 660nm,0.65mm apart two slits, and a screen 1.5m away.Position of n the order fringe = n λ D / d
for n = 2
position = 2 λ D / d
λ = 710 nm , D = 1.5m
d = .65 x 10⁻³
position 1 = 2 x 710 x 10⁻⁹ x 1.5 / .65 x 10⁻³
= 3276.92 x 10⁻⁶ m
= 3.276x 10⁻³ m
= 3.276mm .
For λ = 660 nm
position = 2 λ D / d
λ = 660 nm , D = 1.5 m
d = .65 x 10⁻³
position 2 = 2 x 660 x 10⁻⁹ x 1.5 / .65 x 10⁻³
= 3046.15 x 10⁻⁶ m
= 3.046 x 10⁻³ m
= 3.046 mm .
Difference between their position
= 3.276mm ₋ 3.046 mm
= 0.23 mm .
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Which of the following phrases best describes the term scientific model?
OA. A physical copy of a scientific object, system, or process
B. The application of scientific knowledge to make predictions about
an object, system, or process
C. An experiment in which variables are controlled
OD. A simplified representation used to explain or make predictions
about something
What happens if you move a bar magnet back and forth along the axis of the
coiled wire shown below?
c. A current is induced in the coiled wire, which lights the light bulb.
What is electromagnetic induction?If we kept the bar magnet stationary and moved the coil back and forth within the magnetic field an electric current would be induced in the coil.
Then by either moving the wire or changing the magnetic field we can induce a voltage and current within the coil and this process is known as Electromagnetic Induction and is the basic principle of operation of transformers, motors and generators.
When the magnet shown below is moved “towards” the coil, the pointer or needle of the Galvanometer, which is basically a very sensitive center zeroed moving-coil ammeter, will deflect away from its center position in one direction only.
When the magnet stops moving and is held stationary with regards to the coil the needle of the galvanometer returns back to zero as there is no physical movement of the magnetic field.
Therefore ,
If you move a bar magnet back and forth along the axis of the coiled wire shown below then a current is induced in the coiled wire, which lights the light bulb.
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In the four terrestrial planets, the densest, heaviest materials are at the center and not evenly distributed throughout the planet. Scientists interpret this observation to mean that:
The question is incomplete. Please read below the missing content.
B) The 4 terrestrial planets have to as soon as were hot sufficient to be molten (like a liquid).
Terrestrial planets may be described as any planet of the sun machine or any exoplanet that is "Earth-like" in the experience that it is composed primarily of metals and rock, in evaluation to a planet that's a fuel large.
In the sun machine, the terrestrial planets are the inner planets closest to the solar, i.e. Mercury, Venus, Earth, and Mars.
Scientists believe that the densest, heaviest substances are at the center and not evenly allotted can be due to the truth that they need to once be warm enough to be molten. In this example, density will take region, making the heavier below and the lighter on the pinnacle.
In the four terrestrial planets, the densest, heaviest materials are at the center and not evenly distributed throughout the planet. Scientists interpret this observation to mean that:
a.the four terrestrial planets must once have been inside the Sun
b.the four terrestrial planets must once have been hot enough to be molten (like a liquid)
c.the four terrestrial planets must have formed where Jupiter and Saturn now are
d.the four terrestrial planets must have collided with each other many times
e.none of the above
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The great astronomer of ancient times who summarized and improved a system of circles upon circles to explain the complicated motions of the planets (and published the system in a book now called The Almagest) is:
The great astronomer of ancient times who summarized and improved...in a book now called The Almagest) is Ptolemy This is further explained below.
Who is Ptolemy?Generally, Claudius Ptolemy was a Greek mathematician, astronomer, and geographer who lived in the second century CE and is best known for proposing the geocentric model of the cosmos, which was used to explain planetary and stellar movements for the next thousand years.
In conclusion, Ptolemy, the ancient world's preeminent astronomer, compiled and refined a system of circles inside circles to describe the complexities of planetary motion, publishing his work in what is now known as The Almagest.
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A negatively charged rod is brought rear the cap of a leaf electroscope. The cap is then earthed momentarily by touching with the finger. Finally the rod is withdrawn. The electroscope is found to be positively charged. Explain.
A gold leaf electroscope's cap develops a negative charge when a negatively charged rod is brought close to it; the case is then grounded, creating a negative charge in the leaf. Option D is correct.
What is the charge?When the matter is put in an electromagnetic field, it has an electric charge, which causes it to experience a force. A positive or negative electric charge can exist.
Similar charges repel each other, whereas dissimilar charges attract each other.
The term "neutral" refers to an item that has no net charge. A charge is something experienced as a force in the electric and magnetic fields.
When a negatively charged rod is brought near the cap of a gold leaf electroscope whose case ad then is earthed, then the leaf has an induced negative charge.
Hence option D is correct.
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You have a string with a mass of 0.0135 kg. You stretch the string with a force of 8.29 N, giving it a length of 1.83 m. Then you vibrate the string transversely at precisely the frequency that corresponds to its fourth normal mode, that is, at its fourth harmonic. What is the wavelength of the standing wave you create in the string
The wavelength of the standing wave at fourth harmonic is; λ = 0.985 m and the frequency of the wave at the calculated wavelength is; f = 36.84 Hz
Given Conditions:
mass of string; m = 0.0133 kg
Force on the string; F = 8.89 N
Length of string; L = 1.97 m
1. To find the wavelength at the fourth normal node.
At the fourth harmonic, there will be 2 nodes.
Thus, the wavelength will be;
λ = L/2
λ = 1.97/2
λ = 0.985 m
2. To find the velocity of the wave from the formula;
v = √(F/(m/L)
Plugging in the relevant values gives;
v = √(8.89/(0.0133/1.97)
v = 36.2876 m/s
Now, formula for frequency here is;
f = v/λ
f = 36.2876/0.985
f = 36.84 Hz
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Mature wind waves of one wavelength that form orderly undulations of the ocean surface and often precede a major storm system is known as
Mature wind waves of one wavelength that form orderly undulations of the ocean surface and often precede a major storm system is known as swells.
Meaning of mature wind and waves:
The waves in a fully developed sea outrun the storm that creates them, lengthening and reducing in height in the process.
There are 3 types of wind generated waves:
Capillary wavesGravity wavesSwellswe can say that,
Mature wind waves are known as swell, when they left the formation region.
They have traveled away from where they were raised by the wind, and have to a greater or lesser extent dispersed.
Hence,
Mature wind waves of one wavelength is known as swell.
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Suppose a 60-kg boy and a 41-kg girl use a massless rope in a tug-of-war on an icy, resistance-free surface. If the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.
A.
2.05 m/s2
B.
2 m/s2
C.
2.1 m/s2
Answer:
Approximately [tex]2.05\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
The net force on the girl would be:
[tex]\begin{aligned}m(\text{girl}) \, a(\text{girl}) &= 41\; {\rm kg} \times 3.0\; {\rm m\cdot s^{-2}} \\ &= 123.0\; {\rm N} \end{aligned}[/tex].
Under the assumptions, the net force on this girl would be equal to the tension force in the rope. All other forces on the girl would be balanced.
In other words, the tension force that the rope exerted on the girl would be [tex]123.0\; {\rm N}[/tex]. The girl would exert a reaction force on the rope at the same magnitude ([tex]123.0\; {\rm N}\![/tex]) in the opposite direction. This force would translate to a [tex]123.0\; {\rm N}\!\![/tex] force on the boy towards the girl.
Under similar assumptions, the net force on the boy would also be [tex]123.0\; {\rm N}[/tex]. Since the mass of the boy is [tex]m(\text{boy}) = 60\; {\rm kg}[/tex], the acceleration of the boy would be:
[tex]\begin{aligned}a(\text{boy}) &= \frac{(\text{net force})}{m(\text{boy})} \\ &= \frac{123.0\; {\rm N}}{60\; {\rm kg}} \\ &= 2.05\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
difference between mechanical watch and quartz watch
Answer:
Mechanical vs. Quartz Watch Movements
Mechanical watch movements are powered by gears and springs. They're autonomous little machines without the need for electric power sources, whereas quartz watches are powered by batteries that vibrate little crystals.
A projectile is shot upward from the surface of Earth with an initial velocity of 120 meters per second. What is its velocity after 5 seconds
After 5 seconds the velocity of the projectile is 71m/s
Given that Initial velocity is 120m/s
Time t = 5s
We need to find the velocity after 5 sec
Projectile motion is the movement of an item hurled or projected into the air, which is only subject to the acceleration of gravity. The trajectory of the object is referred to as its trajectory.
The horizontal velocity of a projectile is constant,
There is a vertical acceleration caused by gravity and its value is 9.8 m/s
Now the velocity for 5 seconds
[tex]v(t)=v_0-gt\\[/tex]
[tex]v(t)=120-(9.8)(5)\\\\v(t) =71m/s[/tex]
Hence the velocity after 5 seconds is 71m/s
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A 3600 kg boat is moving with a speed of 2.4 m/s. A much smaller 100 kg jet ski has the same amount of kinetic energy. What is the speed of the jet ski
Answer: A 3600 kg boat is moving with a speed of 2.4 m/s. A much smaller 100 kg jet ski has the same amount of kinetic energy. The is the speed of the jet ski is 14.4 m/s².
Explanation: To find the correct answer to the question given, we need to know more about the Kinetic energy.
What is kinetic energy?It is the form of mechanical energy possessed by a body by virtue of its motion. The expression for kinetic energy of a body of mass m having velocity v can be written as,[tex]KE=\frac{1}{2} mv^2[/tex]
How to solve the problem?Given that the kinetic energy of both the boat and the jet are equal.Let, mass and velocity of the boat will be m1 and v1 and mass and velocity of the jet will be m2 and v2, then,[tex]\frac{1}{2}m_1v_1^{2} =\frac{1}{2}m_2v_2^2\\ Thus, \\v_2^2=\frac{m_1v_1^{2}}{m_2} =207.36\\v_2^2=14.4 m/s^2[/tex]
Thus, we can conclude that, the is the speed of the jet ski is 14.4 m/s².
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If a jumper has a vertical leap of 1.54 m on his trial run, what is their takeoff speed and hang time (total time to move upwards to the peak and then return to the ground)?
The jumper's takeoff speed and hang time are equal to 5.50 m/s and 1.12 seconds respectively.
How to calculate takeoff speed and hang time?In this scenario, the takeoff speed is the same as the initial velocity of the jumper and it can be calculated by using the third equation of motion. Also, since the motion is against gravity, the acceleration due to gravity will be negative (g = -9.81 m/s²)
V² = U² - 2gS
U² = V² + 2gS
U² = 0² + 2(9.81)(1.54)
U = √30.22
U = 5.50 m/s.
Next, we would calculate the peak time by using the first equation of motion:
V = U - at
0 = 5.5 - 9.81t
9.81t = 5.5
t = 5.5/9.81
t = 0.56 seconds.
Mathematically, the hang time is double the peak time:
Hang time = 2 × 0.56
Hang time = 1.12 seconds.
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If for a given pair of media CR
, CY
and CB
are the critical angles for red, yellow and blue colours respectively,
then
CR < CY < CB
Which factors affect the critical angle for a given pair of media?The factors which affect the critical angle are
(a) The colour (or wavelength) of light
(b) The temperature
(i) Effect of colour of light: The critical angle for a pair of media is less for the violet light and more for the red light. Thus the critical angle increases with the increase in wavelength of light.
(ii) Effect of temperature: The critical angle increases with increase in temperature because on increasing temperature of medium, its refractive index decreases.
According to the question,
μ 1 sinCR =1
μ 2 sinCY =1
μ 3 sinCB =1
μ 1 > μ 2 and μ 2 > μ 3
⟹μ 1 > μ 2 > μ 3
CR < CY < CB
Thus,
The critical angle increases with the increase in wavelength of light.
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A radio telescope detects an incoming radio wave which has a power of 1.00 x 10-24 W. If this signal creates a potential of 1.00 nV in the radio receiver, how many electrons move through the receiver circuit per second
Answer:
Therefore, the number of electrons moving through the receiver circuit per second is 6250 electrons/s.
Explanation:
Given:
Power of radio wave, P = 1 × 10⁻²⁴ W
Potential of signal, V = 1 × 10⁻⁹ V
Solution:
Consider the number of electrons flowing through the receiver circuit per second be 'n'.
The current flowing through the circuit will be:
I = P/V
= (1 × 10⁻²⁴ W)/(1 × 10⁻⁹ V)
= 1 × 10⁻¹⁵ A
Then, the number of electrons moving through the receiver circuit can be calculated as:
ne = I
where, e is charge on an electron
I is current flowing through the circuit
Applying values in above equation we get:
n(1.6×10⁻¹⁹ C) = (1 × 10⁻¹⁵ A)
n = (1 × 10⁻¹⁵ A)/(1.6×10⁻¹⁹ C)
n = 6250 electrons/s
Therefore, the number of electrons moving through the receiver circuit per second is 6250 electrons/s.
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