To determine the amount of mechanical energy lost by the brick, we can calculate the initial kinetic energy (KE) and final kinetic energy (KE') and find the difference between them.
The initial kinetic energy (KE) of the brick can be calculated using the formula:
[tex]KE = (1/2) * mass * velocity^2[/tex]
where
mass = 1.50 kg (mass of the brick)
velocity = 13.0 m/s (initial velocity of the brick)
[tex]KE = (1/2) * 1.50 kg * (13.0 m/s)^2[/tex]
KE = 126.45 J
The final kinetic energy (KE') of the brick is zero because it comes to a stop. Therefore, KE' = 0 J.
The amount of mechanical energy lost is given by the difference between the initial and final kinetic energies:
Energy lost = KE - KE'
Energy lost = 126.45 J - 0 J
Energy lost = 126.45 J
So, the brick loses 126.45 Joules of mechanical energy.
This energy is typically converted into other forms, such as thermal energy or sound energy. In this case, the energy lost may primarily be converted into heat due to the presence of the rough surface.
The friction between the brick and the surface generates heat energy, resulting in the loss of mechanical energy.
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You look at a light source through a polarizer. As you turn the polarizer you see no change in intensity. Is the light emitted by this source polarized
No, the light emitted from the source is not polarized
Bypassing it through a polarizing filter or other polarizing substance, light can be made polarized. After passing through a polarizing filter, the intensity of polarized light I is equal to the original intensity I0 cos2, where I0 is the original intensity and is the angle formed by the polarization's direction and the filter's axis.
Unpolarized light is diminished by a factor of 12 when it travels through a polarizer. Along the polarizer's axis, the transmitted light is polarized. The only parameter that is unaffected by any phenomenon, including reflection, refraction, interference polarization, etc., is frequency. The polarization phenomenon has no effect on light frequency.
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Place the charge q= 2.10-5c at the origin o of the oxy-axis system. consider two points a(6;0) and b(3;4) on the axes with unit of measurement in cm. choose the potential origin at infinity. calculate the work done by the electric field when moving the charge q=-1uc from a to b
The work done by the electric field when moving the charge from a to b is 0.0378 J.
Distance between a and b
r = √[(a₂ - a₁)² + (b₂ - b₁)²]
r = √[(3 - 6)² + (4 - 0)²]
r = 5 m
Work done in moving the chargeW = Fr
W = kq₁q₂/r
W = (9 x 10⁹ x 2.1 x 10⁻⁵ x 1 x 10⁻⁶)/(5)
W = 0.0378 J
Thus, the work done by the electric field when moving the charge from a to b is 0.0378 J.
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The amount of straight pipe needed to bend a given radius. Also, the actual length of the conduit that will be bent.
Development length: The actual length of the bent conduit. Gain: Since a conduit bends radially rather than at an angle, the total length will not match the length required for all bends. Gain is the amount of space that is saved by a [tex]90^{0}[/tex] curve.
Bent ConduitConduit benders from Klein Tools are built to function and last longer than even the highest professional standards. To ensure a favourable experience and significantly enhance the final result of your project, it is advised that you become familiar with bending concepts, procedures, and the bender's capabilities. The benders are labelled with various alignment symbols to enable the operator make the bends required to complete any job. This aids bending while executing a ground or air bend. Arrow, teardrop, star point, and angle markings are the symbols on the Klein Tools benders. On certain bender head sides, you can see these markings.
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How much longer (percentage) is a one-mile race than a 1500-m race (""the metric mile"")?
Answer:
1 m = 39.37 in = 3.281 ft
1500 m * 3.281 ft / m = 4922 ft
(5280 - 4922) / 4922 = .073 = 7.3 %
(Note - 1600 m often replaces the 1 mi run)
Which nucleus completes the following equation?
22 Fr He+?
A. 226/85 At
B. 226/89 Ac
C. 222/89 Ac
D. 218/85 At
The nucleus that completes the equation given above is 218/85 At, which is option D.
What is a nuclear fission?Nuclear fission is a nuclear reaction in which a large nucleus splits into smaller ones with the simultaneous release of energy.
According to this question, the following nuclear fission reaction is given: 222/87Fr = 4/2He+ ?
To find the missing nucleus, we subtract 4 from 222 to get 218, therefore, the nucleus that completes the equation given above is 218/85 At.
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The technique called adaptive optics uses dynamic mirror motion to enhance the performance of the new generation of spaced-based telescopes. True False
The mentioned statement is true.
What is adaptive optics(AO)?
Adaptive optics (AO) is a technique that enhances optical systems' performance by minimizing the impact of incoming wavefront aberrations and deforming a mirror to account for the distortion. It is employed in microscopy, optical manufacturing, and retinal imaging systems to lessen optical aberrations and in astronomical telescopes and infrared communication devices to eliminate the impacts of environmental turbulence. Using a technology that adjusts flaws, including a flexible reflector or a liquid crystal array, adaptive optics(AO) measures the abnormalities in a wavefront and adjusts them.How can adaptive optics(AO) enhance a telescope's capabilities?
To counteract the impacts of disturbance, it quickly modifies the telescope mirror's shape.A moderately luminous target star that is adjacent to the target being studied is necessary for adaptive optics. With the use of the deformable mirror, the blurring brought on by the nearby atmosphere is measured using this reference star.Therefore, it is concluded that the mentioned statement is true.
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In the simulation, select the pressure tab, then select the right-most of the three reservoir configurations (top left). By putting weights into the small column of water and using the pressure gauge to measure the water and air pressure, estimate the cross-sectional area of the left column of water. Which of the following best represents the cross-sectional area
The volume of any rectangular solid, including a cube, is calculated mathematically as V = l × w × h
How to find a cross-sectional area?In a given calculation, if you are given the:
Length WidthHeightTo find this, you would have to use the area of its base which is:
Length * Width * Height.
Furthermore, if the cross-section is parallel, then you would have to solve it thus:
Length * Width which is the area of the section from top to bottom.
Although your question is incomplete, the general idea of how to find the cross-sectional area of the volume of any rectangular solid.
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what is the frequency of a wave that has a wavelength of 0.20m and a speed of 22 m/s?
Answer:
f=110HZ
Explanation:
Calculate the frequency of a wave
Based on equation λ= VT but T= 1/f
=> λ=V/f
=> f= V/λ
by V=22m/s
λ= 0.20m
=> f= 22/0.20= 22/(2×10-¹) = 110Hz
So the frequency of a wave is f=110Hz
Answer:
110
Explanation:
velocity=wavelength×frequency
22=0.20f
divide both sides by 0.20
22/0.20=0.20f/0.20
f=22/0.20
f=110
Hull (1943) had rats push a lever that required 21 grams of force to budge. After they had learned to push the lever in order to receive food, he increased the amount of force required to move the lever to 38 grams of force. Which of the following best describes how the rats responded to this new level of required intensity
Years of research have demonstrated that rats are intelligent creatures who experience pain and pleasure, care about one another, are able to read the emotions of others, and would assist other rats, even at their own expense.
Experiments:In trials carried out at Brown University in the 1950s, rats were trained to press a lever for food, but they stopped pressing the lever when they noticed that with each press, a rat in an adjacent cage would scream in pain (after experiencing an electric shock).
Rats were trained to press a lever to lower a block that was hanging from a hoist by electric shocks administered by experimenters. A rat was subsequently hoisted into a harness by the experimenters, and according to their notes, "This animal normally shrieked and wriggled sufficiently while dangling, and if it did not, it was jabbed with a sharp pencil until it exhibited indications of discomfort." Even if it wasn't in danger of receiving a shock, a rat watching the scenario from the floor would pull a lever to lower the hapless rodent to safety.
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use the tools to measure the velocity of the cart after the string was cut. This velocity will be a constant on a smooth surface (after the spring is no longer pulling). What value did you get for the velocity
The value gotten for the velocity after using the use the tools to measure the velocity of the cart after the string was cut is positive
What is velocity?Velocity can simply be defined as the rate of change of displacement with time
Velocity is measured in meters per second (m/s)
So therefore, thee value gotten for the velocity after using the use the tools to measure the velocity of the cart after the string was cut is positive
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A 67 V power supply is connected to three identical resistors in series. If the current through the resistors is measured at 0.95 A, what is the value of each resistor? Round your answer to 2 decimal places.
The value of each resistor is 23.51 ohms.
Value of each resistor
The value of each resistor is calculated as follows;
R₁ = R₂ = R₃ = R
Total resistance, Rt = 3R
V = IRt
V = I(3R)
R = V/3I
R = (67)/(3 x 0.95)
R = 23.51 ohms
Thus, the value of each resistor is 23.51 ohms.
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Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds. approximately how far away is vega from the sun?
Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds, approximately Vega will be 25.076 Light year or 7.692 Parsec away from the sun
The parallax angle is the angle between the Earth at one time of year, and the Earth six months later, as measured from a nearby star.
Mathematically it can be understood as that the parallax angle is the angle which is taken from a point at one time on the earth and again after six months later from the same point on the earth. The parallax angle is the semi-angle of inclination between the two lines to sight.
Stellar parallax is the basis for the parsec, which is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond.
Distance (in parsec) = 1 / (parallax angle ( arcsec))
given
parallax angle = 0.13 arcseconds
Distance (in parsec) = 1/ 0.13 = 7.692 Parsec
if 1 Parsec = 3.26 Light year
So, 7.692 Parsec will be equal to = 3.26 * 7.692 = 25.076 Light year
≈ 25.076 Light year
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A helicopter blade starts to rotate from rest with a constant angular acceleration of 0.82 radians/second2. How many revolutions will the blade make before it is rotating at 500 revolutions per minute (RPM)
Revolutions made by the blade will be 266 rev
Given:
Constant angular acceleration = 0.82 radians/second^2
number of revolution per minute = 500
To Find:
number of revolution
Solution: Angular Acceleration is defined as the time rate of change of angular velocity. It is usually expressed in radians per second per second.
Initial speed of the helicopter blade, w₁ = 0
The final speed of the blade, wf = 500 rpm = 500 x 2π/60 rad/s = 52.35 rad/s
We need to find the number of revolutions. Firstly we will find the angle turned by the blade. Let the angle is θ
So,
wf^2 - wi^2 = 2αθ
θ = wf^2/2α = 1671 rad
Let there are n number of revolutions made by the blade. So,
n = θ / 2π
n = 1671 / 2 x 3.14 = 266 rev
So, the revolutions made by the blade will be 266 rev
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According to the theory of a symmetry breaking, at the moment of quark confinement, when the universe was 10-6 seconds old, what were the relative numbers of neutrons and antineutrons
At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.
What is quark confinement?Note that one quark is never found on its own but if particles are said to be smashed together and quarks are found, they are said to be like ends of rubber bands that expands.
Hence, At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.
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Maryam is driving her car when she glances at the temperature displayed on her dashboard. It says that the temperature is currently 78 degrees outside. This temperature is called a ___.
Answer: Maryam is driving her car when she glances at the temperature displayed on her dashboard. It says that the temperature is currently 78 degrees outside. This temperature is called a Sensation.
Explanation: To find the answer, we need to know more about the Sensation, perception and psychophysics.
What is sensation, perception and psychophysics?Sensation can be defined as the process by which the physical energy from objects in the world stimulates the sense organs.The process in which the brain interprets and organizes this sense of information is called, Perception.The branch of physics that deals with the study of how physical properties of stimuli connected with the people's experience of stimuli is called the Psychophysics.Thus, we can conclude that, the process of sensation happens here.
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a ball is thrown vertically upward with an initial speed of 20 m/s. What is the velocity right before returning to y
The ball's return velocity is (-20 m/s) before reaching its starting location.
According to the 3rd equation of motion-
When an item is propelled higher by gravity, it progressively slows down until it achieves its maximum height.The earth's gravitational pull causes it to turn around after reaching its highest peak and fall freely back to the ground.An object that is falling freely has a starting velocity of "0"
The object accelerates at a rate of "g."
Let 'h' represent the distance the item travels while in free fall.
We can now get the ultimate velocity of the object shortly before it touches the earth with this equation,
v²=u²+2as
Assume that the ball returns to its originating place at "v". Although the ball's orientation changes as it returns to its original place, its speed stays constant.A positive direction should point upward, while a negative direction should point below.Calculation-
For upward motion,
providing that,
The ball's initial speed is u = +20 m/s.
So, v²= u² + 2as
⇒0= (20)² - 2gH [ where 'H' = maximum height reached]
⇒H= 400/2g
For downward motion,
v²=u²+2as
⇒v²= 0²+2g*400/2g
⇒v²= 400 m/s
⇒v= 20 m/s
Therefore, the ball's return velocity is (-20 m/s) before reaching its starting location.
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g Suppose the intensity of some electromagnetic wave doubles. What happens to the amplitude of the wave's electric field?
The amplitude of the wave's electric field is [tex]\sqrt{2}[/tex] times if the intensity of some electromagnetic wave doubles.
What is electromagnetic wave:
Electromagnetic waves also called EM waves, are waves that are created as a result of vibrations between an electric field and magnetic field.
The formula of Intensity of electromagnetic wave:
I = 1/2 ( c* ε(0)* E(0)^2 )where c is speed of light
E is amplitude of electric field
here Intensity of EM waves doubles so,
I' = 2*I
we can say that,
I ∝ E^2
E = sqrt ( I )
E' = sqrt ( 2*I )
hence
E' = [tex]\sqrt{2}[/tex] * E
so, the amplitude of the wave's electric field is [tex]\sqrt{2}[/tex] times if the intensity of some electromagnetic wave doubles
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What is the strength of the intermolecular forces between liquid and gas
A swimming pool is 4.0 m in depth; a swimmer at this depth feels discomfort in the ear. Calculate the net force on a 0.50-cm-diameter eardrum, assuming the inner surface of the eardrum remains at 1 atm pressure
The net force on a 0.50-cm-diameter eardrum is mathematically given as
F= 0.76969 N
What is the net force on a 0.50-cm-diameter eardrum?
Generally, the equation for Pressure is mathematically given as
P = ρgh
Therefore
P= 1000*9.8*4
P= 39200 Pa
Where
A= pi*(0.005/2)^2
Generally, the equation for Net force is mathematically given as
F = PA
F= 39200 *( pi*(0.005/2)^2)
F= 0.76969 N
In conclusion, The net force is
F= 0.76969 N
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A 100-lb child stands on a scale while riding in an elevator. What does the scale read while the elevator slows to stop at the lowest floor
Answer: A 100-lb child stands on a scale while riding in an elevator. Then, the scale reading approaches to 100lb, while the elevator slows to stop at the lowest floor
Explanation: To find the correct answer, we need to know more about the apparent weight of a body in a lift.
What is the apparent weight of a body in a lift?Consider a body of mass m kept on a weighing machine in a lift.The readings on the machine is the force exerted by the body on the machine(action), which is equal to the force exerted by the machine on the body(reaction).The reaction we get as the weight recorded by the machine, and it is called the apparent weight.How to solve the question?Here we have given with the actual weight of the body as 100lbs.This 100lb child is standing on the scale or the weighing machine, when it is riding .During this condition, the acceleration of the lift is towards downward, and thus, a force of ma .There is also mg downwards and a normal reaction in the upward direction.when we equate both the upward force and downward force, we get,[tex]ma=mg-N\\N=mg-ma[/tex] i.e. during riding the scale reads a weight less than that of actual weight.
When the lift goes slow and stops the lowest floor, then the acceleration will be approaches to zero.Thus, from the above explanation, it is clear that ,when the elevator moves to the lowest floor slowly and stops, then the apparent weight will become the actual weight.
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A 5.0-kg object is suspended by a string from the ceiling of an elevator that is accelerating downward at a rate of 2.6 m/s 2. What is the tension in the string
The tension in the string is 36 N.
To find the answer, we need to know about pseudo acceleration.
What's pseudo acceleration?When an object is placed on a vehicle, it experiences a pseudo acceleration in the opposite direction of the motion of the vehicle. Magnitude of the pseudo acceleration is same as that of the acceleration of vehicle.What's the pseudo acceleration of a mass suspended in a lift that's moving downward with an acceleration of 2.6 m/s²?Here, the acceleration of the lift is 2.6m/s², so the mass suspended by a string inside it will feel a pseudo acceleration of 2.6m/s² upward.So the effective acceleration of the mass = acceleration due to gravity - pseudo acceleration = 9.8 - 2.6 = 7.2 m/s²What's the tension of the string suspending the mass?Tension of the string= mass × effective acceleration
= 5 × 7.2 = 36 N
Thus, we can conclude that the tension in the string is 36 N.
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Magnetic field lines point _____ north poles and _____ south poles
Magnetic field lines point leave north poles and enter south poles.
What are Magnetic field lines?This is referred to as the direction that a small compass points when placed at a location.
They are closed curves which runs from the north pole and enters the south pole thereby making it the most appropriate choice.
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1. Determine the energy released per kilogram of fuel used.
Given MeV per reaction, calculate energy in joules per kilogram of reactants.
Consider 1 mole of tritium plus 1 mole of deuterium to be a mole of “reactions” (total molar mass = 5 grams).
2. Determine the mass of fuel required for the expected energy consumption in the United States for the next 10 years.
Energy use per person per year in the United States = 3.5 × 1011 joules.
Base your calculations on a current population of 310,000,000.
1MeV = 1.6 x 10-13 J and 3.5 x 1011 joules of energy is energy in joules per kilogram of reactants.
The amount of fuel needed to meet US expectations for energy consumption over the next ten years.
In the US, each person uses 3.5 x 1011 joules of energy annually. 310,000,000 people make up the present population, thus use 1MeV = 1.6 x 10-13 J in your calculations.
In the US, annual energy consumption per person is equal to 3.5 x 1011Joules (estimated, varies by source, August 2009)
USA population: 310,000,000, roughly.
One mega electron volt, or one million electron volts, is designated as MeV. A particle with one electron charge will gain one MeV of energy when it passes through a potential difference of one million volts in a vacuum.
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The acceleration due to gravity is lower on the Moon than on Earth. Which of the following is true about the mass and weight of an astronaut on the Moon's surface compared to Earth
Mass is the same, weight is less
What is the Weight and mass on Moon ?As we know that the mass of the object is the measurement of the quantity of the matter that is present in it
So here we can say that if the mass of the object is m then its total quantity of the matter that is present in it is given as
mass = (density) × (volume)
Now for the weight of the object is defined as the force of gravity due to planet
Fg = mg
so the weight of the object is depending on the acceleration due to gravity of the planet
As we know that the gravity of moon is smaller than the gravity of the earth so here weight on the moon will be smaller than the weight on the Earth
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Which of the following areas takes visual information from one side of the body and conveys it to the opposite side
The optic chiasm is the point where the optic nerves cross the midline, allowing the opposite side of the brain to process sensory data from one side of the body.
What is the optic chiasm and where is it located?Since the optic nerves cross in the optic chiasm, also known as the optic chiasma, it plays a crucial role in the visual pathway. Within the suprasellar cistern, it is situated 10 mm above the pituitary gland and 10 mm beneath the hypothalamus near the base of the brain.
The optic chiasm's function is to make sure that visual impulses reach both hemispheres of the brain. The thalamus receives and processes the majority of brain impulses, which are then transmitted to various parts of the occipital lobe. Half of each divided optic nerve's fibers travel to the opposing side. Due to the anatomical configuration, injury to the optic nerve system results in particular patterns of vision loss.
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The Trichromatic Theory of Color Vision states there are three different cones that process different wavelengths of light. These wavelengths correspond to the colors: Group of answer choices
These wavelengths correspond to the colors: green, red, blue
What is wavelength:
The wavelength of visible light determines the color that the light appears. Light with the longest wavelength appears red, and light with the shortest wavelength appears violet.
what is The Trichromatic Theory of Color Vision:
Trichromatic theory states that there are three types of receptor cells in the retina, which reacts to the light of three different wavelength.
These receptor cells are responsible for perception of colors.
A spectrally pure or monochromatic color can be produced by a single wavelength.
According to Trichromatic theory of color vision,
The colors are: green, blue and red.
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It is well known that for a hollow, cylindrical shell rolling without slipping on a horizontal surface, half of the total kinetic energy is translational and half is rotational. What fraction of the total kinetic energy is rotational for the following objects rolling brainly
The fraction of the total kinetic energy that is rotational for a uniform sphere is 1/3.
What is kinetic energy?Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.Option (a) [tex]f = \frac{0.5}{1.5} = \frac{1}{3}[/tex]
Option (b) uniform sphere
[tex]f = \frac{2}{7}[/tex]
C) uniform hollow sphere
[tex]f = \frac{2}{5}[/tex]
D) uniform hollow cylinder with inner radius R/2 and outer radius R
[tex]f = \frac{5}{13}[/tex]
that fraction of total energy as rotational energy is given as
[tex]f = \frac{\frac{1}{2}Iw^{2} }{\frac{1}{2}mv^{2} + \frac{1}{2} Iw^{2} }[/tex]
[tex]f = \frac{m k^{2}(\frac{v^{2} }{R^{2} }) }{mv^{2} + m k^{2}(\frac{v^{2} }{R^{2} } )}[/tex]
[tex]f = \frac{\frac{k^{2} }{R^{2} } }{1 + \frac{k^{2} }{R^{2} } }[/tex]
A) uniform Solid cylinder for cylinder we know that
[tex]\frac{k\\ ^{2} }{R^{2} }[/tex] = 0.5
[tex]f = \frac{0.5}{1.5} = \frac{1}{3}[/tex]
B) uniform Sphere for sphere we know that
[tex]\frac{k^{2} }{R^{2} } = \frac{2}{5} \\[/tex]
[tex]f = \frac{0.4}{1.4} = \frac{2}{7}[/tex]
C) uniform hollow sphere for hollow sphere we know that
[tex]\frac{k^{2} }{R^{2} } = \frac{2}{3}[/tex]
[tex]f = \frac{\frac{2}{3} }{\frac{5}{3} } = \frac{2}{5}[/tex]
D) uniform hollow cylinder with inner radius R/2 and outer radius R for annular cylinder
[tex]\frac{k^{2} }{R^{2} } = \frac{5}{8}[/tex]
[tex]f = \frac{\frac{5}{18} }{\frac{13}{8} } = \frac{5}{13}[/tex]
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The complete question is -
It is well known that for a hollow, cylindrical shell rolling without slipping on a horizontal surface, half of the total kinetic energy is translational and half is rotational. What fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface?Part AA uniform solid cylinder.Part BA uniform sphere.Part CA thin-walled hollow sphere.Part DA hollow, cylinder with outer radius R and inner radius R/2.
Dalton's law of partial pressures states that for a mixture of gases, the pressure is the of the partial pressures of the individual gases. (assume that the gases do not react with each other.)
True. The partial pressure of gas that is made up of a mixture of gases is the sum of the individual pressure of the gases.
What is Dalton's law of partial pressure?Dalton's law of partial pressure of gases is one of the gas laws that take into consideration the fact that a gas can be made from a mixture of non-reacting gases.
According to him, if a gas is made as such, the pressure of the gas would be the sum of the individual pressure of the component gases. This means that each gas contributes partially to the overall pressure of the gas mixture.
Thus, if gas A is a mixture of gas B and gas C. The pressure, P, of gas A is given as:
P = Pb + Pc where Pb and Pc are the partial pressure of gases B and C respectively.
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What happens if :
. The test charge is not tiny.
The magnitude of the test charge must be small enough so that it does not disturb the issuance of the charges whose electric field we wish to measure otherwise the metric field will be different from the actual field.
How does test charge affect electric field?As the quantity of authority on the test charge (q) is increased, the force exerted on it is improved by the same factor. Thus, the ratio of force per charge (F / q) stays the same.
Adjusting the amount of charge on the test charge will not change the electric field force.
What is a test charge used for?The charge that is used to measure the electric field strength is directed to as a test charge since it is used to test the field strength. The test charge has a portion of charge denoted by the symbol q.
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A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection
The angle of projection is θ = 53°
What is the angle of projection?The angle between the initial velocity of a body from a horizontal plane through which the body is thrown, is known as angle of projection.Motion in A Plane. Show that there are two angles of projection for which horizontal range is the same. Thus horizontal range is the same for angle of projection θ and α = 90°–θ.The maximum height achieved by a projectile ignoring the air resistance is given by HM=U2Sin2 θ 2g.where U is the initial velocity, θ is the angle of projection and g is the acceleration due to gravity.
R = 3H
R = v²sin2θ/g = 2v²sinθcosθ/2 = 3v²sin²θ/2g
tan θ = 4/3
θ = 53°
So, the angle of projection is θ = 53°
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