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556260047625Test No.:_________00Test No.:_________1228725-9525PHILIPPINE SCIENCE HIGH SCHOOL – Main Campus<br />Physics 2 – Advanced Topics in Physics I<br />LONG TEST 3: PROJECTILE MOTION<br /><ul><li>True or False</li></ul>Direction:<br />Write T if the statement is true and F if it is false. Note that air resistance is neglected in all statements.<br /><ul><li>A projectile fired at any angle above the ground has a constant horizontal velocity in all points.
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The time in going up of a projectile is the same to its time in going down back to its initial level. </li></ul>The range of a projectile is maximum if it is fired at angle of 45o.<br />A projectile fired at an angle of 25o covers the same range if it is fired at an angle of 65o with greater initial speed.<br /><ul><li>The vertical motion of a projectile is a uniformly accelerated motion.
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A projectile is an object launched into space under the influence of gravity only.
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A football is kicked at an angle of θ with respect to the horizontal. The acceleration is -9.8 m/s2 at all times.
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At the highest point of the trajectory, the ball’s velocity is perpendicular to its acceleration.
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A projectile fired horizontally will strike the ground in the same time as one dropped vertically from the same position if we neglect the effects of air resistance.
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The range of a projectile is affected by its initial speed only.
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PROBLEM SOLVING</li></ul>Direction:<br />Solve all the problems completely and correctly in your answer sheet. Always follow the format in problem solving: Illustration (if necessary) -> Given -> Find -> Derivation -> Solution -> Final answer -> Box your final equation and answer. Follow significant figures rules.<br />Problems 01 to 04 pertain to the statement below:<br />A projectile is fired at an angle of 60.0o above the horizontal/ground with an initial speed of 30.0 m/s.<br /><ul><li>(2 points) What is the initial horizontal velocity, vix of the projectile?
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(2 points) What is the initial vertical velocity, viy of the projectile?
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(3 points) How far does the projectile travel horizontally (range), x before it hits the ground?
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(3 points) How long (time) does it take the projectile to reach the highest point in its trajectory?</li></ul>Problems 05 to 08 pertain to the statement below:<br />A shell is fired horizontally in the positive x direction from the top of an 80.0 m high cliff. The shell strikes the ground 1330 m from the base of the cliff.<br /><ul><li>(3 points) Determine the initial velocity of the shell.
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(2 points) What is horizontal velocity of the shell as it hits the ground?
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(2 points) What is vertical velocity of the shell as it hits the ground?
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(3 points) What is the velocity (magnitude and direction) of the shell as it hits the ground? Hint: use your answers in 06 and 07 and apply vector components</li></ul>Problems 09 to 12 pertain to the statement below:<br />A football is kicked with an initial speed vi at an angle θ above the horizontal ground. It covers a horizontal distance/range of 26 m in 3.4 s.<br /><ul><li>(2 points) What is horizontal velocity, vix of the football?
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(2 points) What is the initial vertical velocity, viy of the football?
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(3 points) What is initial speed (magnitude of the velocity) of the football?
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(3 points) What is the angle of trajectory, θ? What is the other angle that can give the same range of the football if it is kicked at the same speed?</li></ul> <br />GOD Bless!!! John 3:16<br />Tract: dtquinsaat_07/31/2010/1832h <br />Answers and Solutions<br /><ul><li>True or False
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A projectile fired at any angle above the ground has a constant horizontal velocity in all points. – T
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The time in going up of a projectile is the same to its time in going down back to its initial level. – T </li></ul>The range of a projectile is maximum if it is fired at angle of 45o. – T <br />A projectile fired at an angle of 25o covers the same range if it is fired at an angle of 65o with greater initial speed. – F <br /><ul><li>The vertical motion of a projectile is a uniformly accelerated motion. – T
20.
A projectile is an object launched into space under the influence of gravity only. – T
21.
A football is kicked at an angle of θ with respect to the horizontal. The acceleration is -9.8 m/s2 at all times. – T
22.
At the highest point of the trajectory, the ball’s velocity is perpendicular to its acceleration. – T
23.
A projectile fired horizontally will strike the ground in the same time as one dropped vertically from the same position if we neglect the effects of air resistance. – T
24.
The range of a projectile is affected by its initial speed only. – F
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PROBLEM SOLVING</li></ul>Problems 01 to 04 pertain to the statement below:<br />A projectile is fired at an angle of 60.0o above the horizontal/ground with an initial speed of 30.0 m/s.<br /><ul><li>(2 points) What is the initial horizontal velocity, vix of the projectile?
26.
(2 points) What is the initial vertical velocity, viy of the projectile?
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(3 points) How far does the projectile travel horizontally (range), x before it hits the ground?
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(3 points) How long (time) does it take the projectile to reach the highest point in its trajectory?</li></ul>Illustration:<br />Given:vi=30.0 m/s- initial velocity magnitude of the projectile<br />θ=60o- angle of projection<br /><ul><li>Find: vix=?- initial horizontal velocity of the projectile
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Substitution:t=-30.0 m/ssin60o-9.8 m/s2t=2.65 s</li></ul>Problems 05 to 08 pertain to the statement below:<br />A shell is fired horizontally in the positive x direction from the top of an 80.0 m high cliff. The shell strikes the ground 1330 m from the base of the cliff.<br /><ul><li>(3 points) Determine the initial velocity of the shell.
42.
(2 points) What is horizontal velocity of the shell as it hits the ground?
43.
(2 points) What is vertical velocity of the shell as it hits the ground?
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(3 points) What is the velocity (magnitude and direction) of the shell as it hits the ground? Hint: use your answers in 06 and 07 and apply vector components</li></ul>Illustration:<br />Given:y=80.0 m- height of the cliff<br />x=1330 m- range<br /><ul><li>Find: vi=?- initial velocity of the shell
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Derivation:vi=vix=xt where y=viyt+12at2 initially, viy=0 m/s
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Substitution:v=-9.8 m/s21330 m2+8-80.0 m22-80.0 mv=334 m/s</li></ul>θ=tan-1-280.0 m1330 mθ=-7o=7o below horizontal<br />Problems 09 to 12 pertain to the statement below:<br />A football is kicked with an initial speed vi at an angle θ above the horizontal ground. It covers a horizontal distance/range of 26 m in 3.4 s.<br /><ul><li>(2 points) What is horizontal velocity, vix of the football?
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(2 points) What is the initial vertical velocity, viy of the football?
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(3 points) What is initial speed (magnitude of the velocity) of the football?
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(3 points) What is the angle of trajectory, θ? What is the other angle that can give the same range of the football if it is kicked at the same speed?</li></ul>Illustration:<br />Given:x=26 m- range reached by the football<br />t=3.4 s- time to cover the range or time of flight<br /><ul><li>Find: vix=?- initial horizontal velocity of the football
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