a particle is projected from a point a with a velocity of 21m/s at an angle of 53.1 degees to the horizontal. one second later another particle is projected at a point 0.3m below a with initial velocity of 31.5m/s at an angle of 36.9 degrees to the horizontal.
(i) prove that the particles collide
(ii) find the time of collision
(iii) find the distance of collision from point of projection
Answer:
(i) Please see graph of the motion of the particles created with MS Excel and the calculations in the following sections
(ii) The time of collision is approximately 1.0 seconds
(iii) The common horizontal distance of point collision from the point of projection is approximately 25.2 meters
Explanation:
The velocity with which the first projectile was fired, v₁ = 21 m/s
The angle to the horizontal the particle is launched = 53.1°
The time at which the other particle was launched = 1 second later
The location from which the other particle was projected = 0.3 m below the first particle
The initial velocity of the second particle = 31.5 m/s
The angle to the horizontal at which the second particle was projected, θ = 36.9°
(i) The height reached, by each of the particle is given as follows;
y = u·t - 1/2·g·t²
For the first projectile, we have;
y = 21·(t₁+1)×sin(53.1°) - 9.81·(t₁+1)²/2 + 0.3
For the second projectile, we have;
y= 31.5·(t₁)×sin(36.9°) - 4.905·(t₁)²
If the two projectiles collide, we get;
21·(t₁+1)×sin(53.1°) - 9.81·(t₁+1)²/2 + 0.3 = 31.5·(t₁)×sin(36.9°) - 4.905·(t₁)²
Using a graphing calculator for simplifying, we get;
-11.93·t₁ + 12.2 = 0
t₁ = 12.2/11.93 ≈ 1.02
Therefore, at time t₁ = 1.02 seconds, after the launch of the second particle, the two particle will be at the same vertical height
However, whereby at the time, t₂, the particles collide, the horizontal distance travelled, 'x', will be equal;
We have;
x = u·cos(θ)·t₁
For the first particle, we have;
x₁₁ = 21 × cos (53.1°) × (t₂ + 1)
For the second particle, we have;
x₂₂ = 31.5 × cos (36.9°) × t₂
At the point of collision, we have;
x₁ = x₂
∴ 21 × cos (53.1°) × (t₂ + 1) = 31.5 × cos (36.9°) × t₂
31.5 × cos (36.9°) × t₂ - 21 × cos (53.1°) × t₂ = 21 × cos (53.1°)
t₂ = 21 × cos (53.1°)/(31.5 × cos (36.9°) - 21 × cos (53.1°) ) = 1.00219236871
t₂ ≈ 1.0 seconds
Given that t₁ ≈ t₂, the particles reach the same height and the same horizontal distance at the same time, t₂ ≈ 1.0 and therefore, they collide.
(ii) The time of collision is found above as t₁ ≈ t₂ ≈ 1.0 seconds
(iii) The horizontal distance of the point of collision from the starting point, 'x', is given as follows;
x = 21 × cos (53.1°) × (1.0 + 1) ≈ 25.2
The horizontal distance of the point of collision from the starting point, x ≈ 25.2 meters
The vertical distance of the point of collision from the starting point of the second particle, 'y', is given as follows;
y = 21 × (1+1)×sin(53.1°) - 9.81 × (1+1)²/2 + 0.3 ≈ 14
The vertical distance of the point of collision from the starting point of the second particle, y ≈ 14 meters
The magnitude of the distance from the starting point of the second particle, r = √(25.2² + 14²) ≈ 28.8
The magnitude of the distance from the starting point of the second particle, r ≈ 28.4 meters.
Electrons move from negative to positive while the voltage flows ________ to _______ .
Answer:
positive to negative.
A prism is made from transparent plastic. In this plastic, light travels at 0.8
in air. Light enters one face of the prism at right-angles as shown.
NOT TO
SCALE
ө
The light just escapes from the sloping face of the prism.
What is angle 0?
A 37°
B
390
С
510
D
53°
Answer:
Real answer is im sorry if im wrong
Explanation:
A 53°
The value of the angle Θ will be 51.3°. Option C is correct.
What is the definition of geometry?It is concerned with the geometry, region, and density of various 2D and 3D shapes.
From snell's law;
[tex]\rm n= \frac{sini}{sinr} \\\\ 0.8= \frac{sin(90-\theta)}{sin \theta} \\\\ 0.8= cot \theta \\\\ \theta= cot^{-1} (0.8)\\\\ \theta =51.3^0[/tex]
The value of the angle Θ will be 51.3°.
Hence,option C is correct.
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Un engrane que gira con una velocidad de 20 rad/s, es acelerado durante 5 segundos hasta alcanzar una velocidad de 35 rad/s
a) ¿Cuál es la magnitud de su aceleración angular?
b) ¿Cuántos radianes gira en ese tiempo?
c) ¿Cuántas revoluciones alcanza a girar en ese tiempo?
no m ignoren
Answer:
a) La aceleración angular es: [tex]\alpha=2\: rad/s^{2}[/tex]
b) El engranaje gira 125 radianes.
c) El engranaje hara aproximadamente 20 revoluciones.
Explanation:
a)
La aceleración angular se define como:
[tex]\alpha=\frac{\Delta \omega}{\Delta t}[/tex]
Donde:
Δω es la diferencia de velocidad angular (en otras palabras ω(final)-ω(inicial))Δt es el tiempo en el que occure el cambio de velocidad angular[tex]\alpha=\frac{35-25}{5}[/tex]
[tex]\alpha=2\: rad/s^{2}[/tex]
b)
El desplazamiento angular puede ser calculado usando la siguiente ecuación:
[tex]\theta=\theta_{i}+\omega_{i}t+\frac{1}{2}\alpha t^{2}[/tex]
Aqui el angulo inicial es 0, por lo tanto.
[tex]\theta=20(5)+\frac{1}{2}(2)(5)^{2}[/tex]
[tex]\theta=125\: rad[/tex]
El engranaje gira 125 radianes.
c)
Lo que debemos hacer aquí es convertir radianes a revoluciones.
Recordemos que 2π rad = 1 rev
Entonces:
[tex]\theta=125\: rad \times \frac{1\: rev}{2\pi\: rad}=19.89\: rev[/tex]
Por lo tanto el engranaje hara aproximadamente 20 revoluciones.
Espero te haya sido de ayuda!
Calculate V1 and V2 ( V = voltage )
Given that Vs = 16V, R1 = 330Ω, and R2 = 470Ω
Please do not answer if you don't know how to do this
Calculate V1 and V2 ( V = voltage )
Given that Vs = 16V, R1 = 330Ω, and R2 = 470Ω
Solution:Given that,
Vs = 16VR1 = 330ΩR2 = 470Ω.°.
V1&V2↷
Firstly, we'll find the Total resistance of the circuit=> 330Ω + 470Ω =800Ω
Now, we'll use the ohm's law to calculate the current flow in the circuitVˢ= IRᵀ
[tex]I= \frac{16}{800} = > \frac{1}{50}[/tex]
= 1/50 Ampere
Now,
V1 = IR
[tex]v1 = \frac{1}{50} \times 330 = > 6.6 \: Volt\ \\ v2 = \frac{1}{50} \times 470 = > 9.4 \: Volt[/tex]
______
Hope it helps
-------☆ﾟ.･｡ﾟᵴɒƙυᴚᴀ_ƨȶäᴎ❀
A bucket is held up by a rope.
What force is pulling the bucket down?
O Force Gravity
O Force Tension
O Force Elastic
O Force Normal
Answer:
gravity...................
Answer:
Force GravityHope it help you
Consider the electric force between a pair of charged particles a certain
distance apart. By Coulomb's Law:
If the charge of one of the particles is doubled, the force is:
(unchanged), (halved), (doubled), (quadrupled)
Answer:
Doubled
Explanation:
F = (kq1q2) / r^2
F and q (Either q1 or q2) are directly proportional, so double the charge would also double the electruc force between the charges.
HELP MEEEEE
(science)
Answer:
Decreases the friction between the mallet and the pick.
please help I got no time!!
Answer:
42a. Ammeter 2 = 0.20 A
42b. Ammeter 3 = 0.20 A
42c. The current will remain the same i.e unchanged.
43. Equivalent resistance is 11780 Ω
46a. 11 V
46b. 7.5 V
46c. 18.5 V
47. 1.70 A
Explanation:
42a. Determination of ammeter 2
Ammeter 1 = 0.20 A
Ammeter 2 =?
Since the resistors are in series connection, the same current will pass through them. Thus, ammeter 2 will read 0.20 A.
Ammeter 2 = ammeter 1 = 0.20 A
42b. Determination of ammeter 3
Ammeter 1 = 0.20 A
Ammeter 3 =?
Since the resistors are in series connection, the same current will pass through them. Thus, ammeter 3 will read 0.20 A.
Ammeter 3 = ammeter 1 = 0.20 A
42c. Since the resistors are in series connection, the same current will pass through them. Therefore, the current will remain the same.
43. Determination of the equivalent resistance.
We'll begin by converting 1.1 KΩ and 10 KΩ to Ω. This can be obtained as follow:
1 KΩ = 1000 Ω
Therefore,
1.1 KΩ = 1.1 KΩ × 1000 Ω / 1 KΩ
1.1 KΩ = 1100 Ω
1 KΩ = 1000 Ω
Therefore,
10 KΩ = 10 KΩ × 1000 Ω / 1 KΩ
10 KΩ = 10000 Ω
Finally, we shall determine determine the equivalent. This can be obtained as follow:
Resistor 1 (R₁) = 680 Ω
Resistor 2 (R₂) = 1100 Ω
Resistor 3 (R₃) = 10000 Ω
Equivalent Resistance (Rₑq) =?
Rₑq = R₁ + R₂ + R₃
Rₑq = 680 + 1100 + 10000
Rₑq = 11780 Ω
Thus, the equivalent resistance is 11780 Ω
46a. Determination of the voltage across 22 Ω
Current (I) = 0.50 A
Resistor (R₁) = 22 Ω
Voltage (V₁) =?
NOTE: the current is the same since the resistor are in series connection.
V₁ = IR₁
V₁ = 0.5 × 22
V₁ = 11 V
46b. Determination of the voltage across 15 Ω
Current (I) = 0.50 A
Resistor (R₂) = 15 Ω
Voltage (V₂) =?
NOTE: the current is the same since the resistor are in series connection.
V₂ = IR₂
V₂ = 0.5 × 15
V₂ = 7.5 V
46c. Determination of the voltage of the battery.
Voltage 1 (V₁) = 11 V
Voltage 2 (V₂) = 7.5 V
Battery voltage (V) =?
V = V₁ + V₂
V = 11 + 7.5
V = 18.5 V
47. Determination of the current.
We'll begin by calculating the equivalent resistance. This can be obtained as follow:
Resistor 1 (R₁) = 22 Ω
Resistor 2 (R₂) = 4.5 Ω
Equivalent Resistance (R) =?
R = R₁ + R₂
R = 22 + 4.5
R = 26.5 Ω
Finally, we shall determine the current.
Voltage (V) = 45 V
Resistance (R) = 26.5 Ω
Current (I) =?
V = IR
45 = I × 26.5
Divide both side by 26.5
I = 45 / 26.5
I = 1.70 A
As Jack pulls his wagon down the street it moves faster and faster. Jill, sitting a few meters ahead on the sidewalk, wants to slow Jack's wagon down so that it travels with a constant speed. How can Jill accomplish her goal? A) Push the wagon with a force greater than Jack. B) Push Jack away from the wagon so that he is no longer pulling it. C) Pull on the wagon in the opposite direction with twice Jack's force. D) Push the wagon in the opposite direction at a constant force less than Jack.
Answer:
The correct answer is NONE the two forces must be equal and of opposite direction, the closest answer is D
Explanation:
In this exercise it is indicated that Jack pushes a car, it is desired that Jill pushes the car so that the speed is constant
take as positive the direction of Jack's thrust
F_jack - F_jill = 0
F_jill = F_jack
therefore the push of the two must be equal and Jill's push must have the opposite direction to Jack's push.
The correct answer is NONE the two forces must be equal and of opposite direction, the closest answer is D
1. An object of mass 300 kg is observed to
accelerate at the rate of 1 m/s. Calalate the
force required to produce this acceleration.
Answer:
The force required will be "300 N".
Explanation:
The given values are:
Mass of object,
m = 300 kg
Acceleration,
a = 1 m/s
Now,
The force will be:
⇒ [tex]F=m\times a[/tex]
On substituting the values, we get
⇒ [tex]= 300\times 1[/tex]
⇒ [tex]=300 \ N[/tex]
If a balloon has 12 electrons on its surface but also 13 protons, what
is the net charge on the balloon?
Answer:
q = 1
Explanation:
Given that,
No. of electrons = -12
No. of protons = 13
We need to find the net charge on the balloon. We know that net charge is equal to the sum of proton and the electrons such that,
Net charge = No. of electrons + no. of protons
= -12 + 13
= 1
So, the net charge is equal to 1.
You have two photos of a person walking. One shows the person at the corner of Third and Main streets, the other shows the person at the corner of Tenth and Main streets. There are lampposts at every corner in this town, and the first picture shows it to be 10:32:00 exactly. The second picture shows it to be 10:49:30. You know three facts: (1) All of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross Main in this area are numbered consecutively, with no interruptions. What is the person’s average speed in kilometers per hour?
Answer:
average speed
= [(10-3)/12 km] / [(49.5-32.0)/60 hour]
= 5*7 / 17.5
= 2 km/h .
1.
You just earned a $1000 bonus at your job. Would you rather receive all the money at the end of the
year or half the money now and half the money later? Why?
Which wave must have a medium to travel?
A) light wave
B)compression wave
C) electromagnetic wave
D) ultraviolet wave
*****Urgent****
Letter B
without a medium, there is nothing to compress, hence, no wave. A fast- medium like a gas (air) is easy to compress and allows waves to move through it easily. a slow medium, like a liquid, is still pretty fast, but not as fast as air.
the body acts on a force of 3N with the shoulder 20 cm. What is her moment?
Answer:
0.6Nm
Explanation
Given
Force = 3N
Distance = 20cm = 0.2m
Moment = Force * perpendicular distance
Substitute
Moment = 3N * 0.2
Moment = 0.6Nm
Hence her moment is 0.6Nm
If a ball is lifted 2 meters off the ground and 5 Newtons of force were needed to move it,
what amount of work has been done? :3
Answer:
W = 98 J
Explanation:
Given hat,
Force, F = 5 N
It is lifted 2 m off the ground.
We need to find the amount of work done. We know that, the work done by an object is given by the product of force and displacement. So,
W = Fd
or
W = mgd
Put all the values,
W = 5 × 9.8 × 2
W = 98 J
So, the work done is equal to 98 J.
which process is the source of most oxygen in the atmosphere
Answer:
photosynthesis
The air that enters human lungs contains about 21 percent oxygen. The process responsible for producing most of the Earth's oxygen is known as photosynthesis. In this process, plants and certain other organisms convert sunlight into oxygen and other products.
Explanation:
Hope it helps! Correct me if I am wrong!
I'm sure about my answer!
If you dont mind can you please mark me as brainlest?
Its ok if you don't want to!
But i hopefully it helps you!
Answer:
Photosynthesis I think
Explanation:
Four different living organisms are shown on the right. Which statement is true for all of the organisms shown?
Answer:
they are all made of cells
What chemical formula did early instigators assume for water?
Answer:
Explanation:
Investigators thought this meant that oxygen was eight times more massive than hydrogen. They presumed the chem-ical form-ula for water to be H-O
Hope this helped!!! .
Which of the following regions of the EM epxtrum has the highest
frequency?
1) x rays
2) microwaves
3) infrared light
4) ultraviolet light
Answer:
1) x rays
Explanation:
Honestly Gamma rays has the Highest frequency, but in your options, gamma rays is not among, so x rays has the highest frequency among your options.
by Manshow
Answer:
The answer is (X-rays)
number 1
How is it possible a plant can sustain itself for 70 years locked inside a jar?
Answer:
If you are talking about the experiment in which mouse and plants are kept in a closed glass jar in sunlight so in that case, they both survive because the CO2 released by the respiration of mouse is being utilized by the plants and fixed ( phosynthesis) and O2 is released as by product, which is taken by the mouse for respiration.
Explanation:
How energy is converted from one form to other
Explanation:
Energy can be converted from one form to another. Examples: Gasoline (chemical) is put into our cars, and with the help of electrical energy from a battery, provides mechanical (kinetic) energy. ... Similarly, purchased electricity goes into an electric bulb and is converted to visible light and heat energy.
Answer:
Explanation:
Energy transformation is when energy changes from one form to another. While energy can be transferred or transformed, the total amount of energy does not change – this is called energy conservation. For example, Electricity goes into an electric bulb and is converted to visible light and heat energy.
Hope this helped!!!
Consider again the civilization described in the previous question. (They live on a planet orbiting 10 AU from a close binary star system that consists of a 15 MSun red giant star and a 10 MSun black hole surrounded by an accretion disk.) Through a bizarre (and scientifically unexplainable) fluctuation in the space-time continuum, a copy of a book from that civilization arrives on your desk; it is entitled Iguoonos: How We Evolved. In the first chapter, you learn that these beings evolved from organisms that lived 5 billion years ago. Which of the following statements should you expect to find as you continue to read this book?
A. Their immediate ancestors were chimpanzees.
B. As a result of traumatic experiences to their evolutionary ancestors, they dislike television.
C. They evolved on a different planet in a different star system, and moved to their current location.
D. They evolved from primitive wormlike creatures that had 13 legs, 4 eyes, and bald heads, thus explaining why such critters are now considered a spectacular delicacy.
E. They believe that the presence of two stars in their system was critical to their evolution.
In the compound MgCl2, how many atoms of Mg are there?
Energy ___________.
is used to do work
can't be converted from one form to another
can be created or destroyed
Answer:
BRAINLIEST PLSSSSSSSSSSSSSSSSSSSSSSSS
Thermodynamics
Explanation:
Thermodynamics is the study of energy. First Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another.
It takes 5000 J of work to lift a crate to a height of 5 m in 10 s of time.. Calculate the power.
Answer:
P = 500 W
Explanation:
Given that,
Work done to lift a crate to a height of 5 m is 5000 J
It takes 10 s
We need to find the power of the crate. We know that power is the rate of doing work. Mathematically, it can be given by :
[tex]P=\dfrac{W}{t}\\\\P=\dfrac{5000}{10}\\\\P=500\ W[/tex]
So, the power of the crate is equal to 500 W.
How you work out efficiency?
Answer:
The work efficiency formula is efficiency = output / input, and you can multiply the result by 100 to get work efficiency as a percentage. This is used across different methods of measuring energy and work, whether it's energy production or machine efficiency.
Explanation:
Hope this helped!!!
What is the best way for the power plant manager to modify the reactor to meet the demand for electricity? lower the control rods, which will absorb more neutrons before they can split atoms raise the control rods so that fewer neutrons are absorbed and more can split uranium atoms remove some of the fuel rods, which will leave more room for additional neutrons to split atoms add additional fuel rods to generate additional neutrons to split uranium atoms
The question is incomplete, the complete question is;
During a heat wave, there is an increased demand for electricity to operate air conditioners. The basic design of a nuclear reactor that generates electricity is shown below. What is the best way for the power plant manager to modify the reactor to meet the demand for electricity?
a)lower the control rods, which will absorb more neutrons before they can split atoms
b)raise the control rods so that fewer neutrons are absorbed and more can split uranium atoms
c)remove some of the fuel rods, which will leave more room for additional neutrons to split atoms
d)add additional fuel rods to generate additional neutrons to split uranium atoms
Answer:
b)raise the control rods so that fewer neutrons are absorbed and more can split uranium atoms
Explanation:
A nuclear reactor uses a nuclear fuel to generate electricity. The nuclear reactor makes use of a fissile isotope such as Uranium-235 as nuclear fuel which is bombarded by neutrons and causes a nuclear fission to occur leading to a consequent initiation of a chain reaction.
Control rods are used to absorb some of the neutrons and keep the reaction under control.
When there is need to increase power generation, the control rods are raised so that less neutrons are absorbed by them and more of the uranium fuel is split.
A person pushes a 125 kg object initially at rest on a frictionless surface. The object ends up with a final velocity of 1.40 m/s. What is the total
translational kinetic energy of the object?
Answer:
a person pushes a 125 kg
Explanation:
The total translational kinetic energy of the object is 122.5 J.
What is meant by kinetic energy ?Kinetic energy is defined as the energy possessed by a body by virtue of its motion.
Here,
Mass of the object, m = 125 kg
The final velocity of the object, v = 1.4 m/s
It is given that the object was initially at rest on a frictionless surface. When the object was pushed by the person, it gained some amount of kinetic energy and ended up with a final velocity of 1.4 m/s.
So, the expression for total translational kinetic energy of the object is given by,
KE = KEf + KEi
KE = 1/2m(v² + u²)
Since, the object was initially at rest, the initial velocity,
u = 0
Therefore, the kinetic energy of the object,
KE = 1/2 mv²
KE = 1/2 x 125 x (1.4)²
KE = 122.5 J
Hence,
The total translational kinetic energy of the object is 122.5 J.
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