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Curvilinear Motion – Projectiles

 

  1. A bomb is dropped from an airplane flying at 250 mi/hr while the plane is at an elevation of 4500 ft when it is directly over the target.  How far will the bomb miss the target?
  1. A ball is thrown upward at an angle of 30º with the horizontal.  If the initial velocity of the ball is 256 ft/sec,
    1. How high does it rise?
    2. How long will it be in the air?
    3. How far horizontally does it travel?
  1. A man stands at the edge of a cliff 59 m in height.  He throws a ball upward at an angle of 40º with the horizontal and with an initial velocity of 1600 m/sec.  Find:
    1. How long was the ball in the air?
    2. How far vertically did the ball rise?
    3. With what velocity does the ball strike the ground at the base of the cliff?
    4. How far horizontally did the ball travel?
  1. A discus is thrown a horizontal distance of 160 m when it is thrown at an angle of 35º with the horizontal.  If the discus is to travel 5 m further the next time that it is thrown, at what angle must it be thrown if it is to maintain the same initial velocity as the first time that it was thrown?
  1. A catapult throws a projectile at a target from a cliff 250 m high, with a velocity of 95 m/sec, and at an angle of 20º with the horizontal.  Find:
    1. What was the total time it was in the air?
    2. How far horizontally did it travel from the point of projection?
    3. What maximum height did it attain?
    4. With what velocity did it strike the ground?
  1. A ball is thrown with a velocity of 60 m/sec and it reaches a height of 118 m.  Find:
    1. How long was it in the air?
    2. What was the angle of departure?
    3. What was its range of flight?
  1. A bullet is fired into the air with a muzzle velocity of 118 m/sec and angle of 40º.
    1. How long will it be in the air?
    2. How far does it travel horizontally?
    3. How high will it rise?
  1. A ball is thrown with a horizontal velocity of 80 m/sec from the top of a 250 m high building.
    1. How long will it be in the air?
    2. How far from the base of the building does it strike?
    3. With what velocity does it strike?
  1. A bullet is shot upward at an angle of 45º with the horizontal and with a velocity of 1630 ft/sec.  At what two instants will it be 16,640 ft above the Earth?
  1. A ball is thrown upward at an angle of 15º with the horizontal and with a velocity of 68 m/sec.
    1. How high does it rise?
    2. How far horizontal does it travel?
    3. How long is it in the air?
  1. A javelin is thrown with a velocity of 35 m/sec at an elevation angle of 42º.
    1. What maximum height does it attain?
    2. What is its range.
    3. How much farther and higher would it travel if it had been thrown at an angle of 45º?
  1. A mortar hurls a 100-lb shell with a velocity of 600 ft/sec.  Neglecting air resistance, at what angle must it be thrown to hit a target 2000 yards away?
  1. A baseball player throws a ball at the optimum angle to his teammate.  If the ball is in the air for one second,
    1. How high does it rise?
    2. How far away is the teammate?
    3. How fast is it thrown?           
  1. An arrow is shot with a velocity of 200 ft/sec and reaches an altitude of 480 ft.
    1. How long is it in the air?
    2. What elevation angle is utilized?
    3. What is its range?
  1. A catapult hurls a stone at an elevation angle of 30º from the top of a cliff, which is 400 m above the edge of a lake.  The initial velocity of the projectile was 43 m/sec.
    1. What maximum height does it attain above the water?
    2. With what velocity does it strike the water?
    3. How long was it in the air?
  1. An anti-aircraft gun fires a shell at an angle of 55º at an airplane at an elevation of 4000 m.  What minimum velocity must the shell have to enable it to hit the airplane?
  1. A stone is thrown with a velocity of 40 m/sec at an elevation angle of 60º.
    1. What is the position of the stone, horizontally and vertically, after 3 seconds?
    2. What is its total velocity after 3 seconds?
  1. A baseball player throws a ball a distance of 200 ft at the optimum angle.  What minimum velocity must the ball must have to travel this distance?
  1. A man hangs on to the wing of an airplane which is rising from the ground with a constant velocity, the vertical component of which is 10 ft/sec.  After a few moments, he fall off and hits the ground 10 seconds after separating from the plane.  How far above the ground was he when he fell off the plane?
  1. A ball is thrown upward at an angle of 30º with the horizontal, and with an initial velocity of 64 m/sec.
    1. How high will it rise?
    2. How far horizontally will it travel?
  1. A cannon ball is shot upward at an angle of 53º and with a velocity of 1800 ft/sec.  At what two instants will it be 12,000 ft above the Earth?
  1. A supply plane flying in straight and level flight at 210 mi/hr and at an elevation of 480 ft, releases a large bundle of food, which is intended to land on a ground marker.  How far in advance of the marker, as measured along the ground, must the bundle be released?
  1. A shot put is tossed a distance of 52 ft.  The angle of projection used was 40º.  How much more (or less) horizontally would it have traveled if it had been thrown at:
    1. 45º
    2. 50º
  1. A smooth round stone is thrown from a sling with a velocity of 49 m/sec.  At what elevation angle should it be thrown to obtain a range of 245 m?
  1. A 16-inch naval gun produces a muzzle velocity of 2000 ft/sec?
    1. What is its maximum theoretical range?
    2. How long can its projectile remain in the air?
    3. What maximum height can the projectile attain?
  1. A model rocket leaves the ground with a velocity of 160 ft/sec and reaches an altitude of 320 ft.
    1. What will be the duration of the rocket’s flight?
    2. What must be its angle of departure?
    3. What is its maximum possible range?
  1. A howitzer blasts a round at an emplacement on the top of a 120 m high cliff.  The round is fired with a velocity of 250 m/sec and at an angle of 35º.
    1. Is the projectile successful in reaching the top of the cliff if the cannon is located 30 m from the face of the cliff?
    2. If the emplacement is at the leading edge of the cliff, will the round hit the target?
    3. What adjustments must be made for it to hit the target, if it were initially to miss?
  1. An anti-aircraft gun fires at an enemy plane that is at an elevation of 12000 ft.  The gun has a projection angle of 55º and the plane is in level flight.
    1. What must be the muzzle velocity of the shell if it is to hit the plane?
    2. Is there more than one possible muzzle velocity?  If there are, explain.
  1. A stone is thrown with a velocity of 40 m/sec at an elevation angle of 60º.
    1. What is its position after 3.5 seconds?
    2. What is its velocity after 3.5 seconds?
  1. A mail plane traveling at 180 mi/hr comes down to an elevation of 300 m where is straight and level flight, it releases a mailbag to be caught in a net on the ground.  What horizontal distance from the net must the bag be released?
  1. A man pushes a boulder off the top of a 250 m high cliff, it lands at the base of a house 80 m from the base of the cliff face.
    1. How long was it in the air?
    2. With what velocity was it pushed?
    3. With what velocity did it strike the roof?
  1. A ball it thrown horizontally from the top of a building and it strikes the ground in 3.6 seconds.
    1. How high was the building?
    2. With what velocity was it thrown?
    3. With what velocity did it strike the ground 40 m from the building?
  1. A gun with a muzzle velocity of 350 m/sec, fires its bullets horizontally from the top of a building 250 m in height.  What is the bullet’s position after the following time intervals:
    1. 0.75 sec
    2. 1.25 sec
    3. 2.0 sec
    4. 4.50 sec
    5. 6.75 sec
    6. 7.00 sec
    7. 7.50 sec
  1. A cannon is mounted on a hill 150 m high with its barrel pointed horizontally.  It is trying to hit the gate of a city on the plain below which is located a horizontal distance of 350 m away.
    1. What should be the velocity of the cannon ball as it emerges from the muzzle?
    2. How long will it be in the air?
    3. With what velocity will it strike?
  1. An engine accidentally falls off an airplane when it is at an elevation of 4,500 m.  The plane was in level flight and was flying at an unknown velocity.  The engine struck the ground 1,465 m horizontally from where it fell off.
    1. How fast was the plane flying?
    2. What was the velocity of the engine when it struck?
    3. What was the velocity of the engine 25 seconds after it fell from the plane?
  1. A stone is thrown from the top of a building with a horizontal velocity of 92 m/sec and it strikes the ground in 8.0 seconds.
    1. How high is the building?
    2. How far from the base does it strike?
    3. With what velocity was it traveling when it hit?
  1. A rifle is fired so that its shell is projected horizontally toward a target 2,000 yards away.  The target is located at a point 500 ft below where the rifle is located.
    1. How long will it take the shell to reach the target?
    2. What is the muzzle velocity of the shell?
    3. What is the position of the shell 3.5 seconds after being fired?
  1. A hot air balloon is level flight loses one of its ballast sandbags.  The sandbag strikes the ground in 12 seconds and 9,800 ft horizontally from where it was lost.
    1. What was the velocity of the sandbag what it struck?
    2. What was the sandbag’s position 8.0 seconds after it fell?
  1. In attempting to run a cable across a canyon 650 ft deep and 540 ft wide, the electric company fastens one end of a fine wire to an arrow and the other end to the cable which in turn will be pulled across.  The arrow is then projected toward the other side of the canyon with a velocity of 420 ft /sec at an angle of 40º
    1. Where will the arrow strike?
    2. How long will it be in the air?
    3. With what velocity does it strike?
  1. A shot put is tossed at an angle of 40º with a velocity of 58 m/sec.
    1. How much farther, or shorter, would it have gone if the angle were increased by 10º?
    2. Which angle will give the greatest time in the air?
    3. Which one will attain the greatest elevation?
  1. A stone is pushed off a 450 m high cliff and lands on the roof of a building located 88 m horizontally from the base of the cliff.
    1. With what velocity must the stone be pushed?
    2. What was the total time that it was in the air?
    3. With what velocity does it strike?
  2. A javelin is thrown into the air at an angle of 40º and reaches a range of 120 m.
    1. What elevation does it attain?
    2. How long was it in the air?
    3. What was its projection velocity?
  1. A shell is fired from the top of a building with a horizontal velocity of 95 m/sec and it strikes in 7.5 seconds.
    1. What is the height of the building?
    2. How far does it strike from the base of the building?
    3. With what velocity does it strike?
  1. A skydiver is about to leave the plane when he loses a spare helmet kept in the plane.  The helmet strikes in 9.0 seconds and 3,200 m horizontally as measured along the ground.
    1. With what velocity did it strike the ground?
    2. What was the plane’s elevation?
    3. What was the position and velocity of the helmet 8.2 seconds after it fell from the plane?
  1. A brakeman on the roof of a freight car moving at the rate of 50 km/hr throws a stone vertically upward (relative to the train) with an initial velocity of 26 m/sec.
    1. Find the velocity of the stone at the end of 2.0 sec.
    2. Find the distance the train moves while the stone is in the air during the two second interval.
  1. A baseball thrown at an angle of 43º with the horizontal has a range of 80 m
    1. What was the magnitude of its initial velocity?
    2. How high did it rise?
    3. What was its time of flight?

    (#47 removed)

  1. A level-flight forestry service bomber, flying at 120 m/sec, releases a tank of water 2100 m above the ground
    1. How long will it take the water to reach the ground?
    2. How far horizontally has the water traveled?
    3. What will be the striking velocity of the water?
  1.  A batter hits a pitched ball at a height of 1.0 m above the ground.  The ball leaves the bat at an angle of 47º above the horizontal and would travel 113.0 m horizontally before striking the bleachers 1.0 m above the ground.  The ball is fair down the left field line where a 10.0 m high fence is located 107.0 m from home plate.  By how much will it clear or at what height will it strike the fence?
  1. A ball thrown by a boy on the porch of a house is caught 1.8 sec later by another boy in the street 14 m away and 4.0 m below the level of the porch.  What was the speed of the ball and the angle above the horizontal at which it was thrown?
  1. A ball player throws a ball a distance of 65 m.  If the ball reaches a maximum height of 35 m,
    1. What was the magnitude of its initial velocity?
    2. What was the total time of flight?
    3. At what angle theta was the ball thrown?
  1. A baseball player hits a ball such that the ball’s initial velocity is 15 m/sec at 36º above the horizontal.
    1. What is the ball’s horizontal and vertical velocity 0.2 sec after it was thrown?
    2. How much time would the left fielder have to reach the ball and make a shoe string catch?
  1. An infantry wireman is required to lay a wire line across a wide canyon.  He decides to shoot the line across with a grenade launcher.  If the canyon is 200 m wide and there is no wind resistance, what angle should he use if the initial speed of the projectile is 100 m/sec?
  1. During a luncheon in the cafeteria, a student decided to project a cube of butter at another student’s plate 100 m away.  The first student placed the butter on the end of his knife and fire it at an angle of 49º above the horizontal.  Assuming the student scored a direct hit,
    1. How fast was the cube of butter traveling when it left the knife?
    2. How long was the butter in the air?
  1. A forest service water bomber in level flight releases the water from its tank, and reaches the ground in 5.6 sec.
    1. How fast was the plane flying?
    2. What was the plane’s elevation?
    3. With what velocity does the water strike the ground?
  1. A brakeman is on the roof of a freight car 18 ft in height, which is traveling at 40 mi/hr.  The brakeman throws a stone with a velocity of 20 ft/sec perpendicular to the velocity of the train.
    1. With what velocity will the stone strike the ground?
    2. How long does it take the stone to reach the ground?
    3. How far does the train travel while the stone is in the air?
  1. A 180-lb mountain climber throws a stone horizontally from the top of a 125 ft cliff.  When he threw the stone, he slipped and fell over the edge of the cliff. The stone struck the ground 53 ft from the base of the cliff face.  Find:
    1. The velocity with which the stone was thrown.
    2. The velocity with which the stone struck.
    3. The time differential between when the mountain climber and the stone struck the ground.
  1. A golf ball leaves the tee with a velocity of 50 m/sec at an angle of 36º above the horizontal.  It strikes the green at a horizontal distance of 220 m from the tee, but which is not on the same horizontal plane as the tee.
    1. What was the difference in height between the tee and the green?  Is it above or below the level of the tee?
    2. What was the velocity of the ball as it struck the tee?
    3. What was the total time that the ball was in the air?
  1. A ball player throws a ball a distance of 65 m and it was in the air for 4 seconds.
    1. What was the initial velocity of the ball?
    2. What was the angle of the projection of the ball?
    3. What was the maximum height the ball rose above the playing field?
  1. The projectile of an 81 mm mortar has a muzzle velocity of 100 m/sec.
    1. What two angles of elevation above the horizontal enable the projectile to hit a target 900 m away and on the same elevation as the mortar?
    2. What maximum height does the projectile attain?
    3. How much time does the projectile remain in the air?
  1. An apple thrown by a boy on a ladder is caught 3.2 seconds later by another boy on the ground 14 ft away and 4 ft below the level of the boy on the ladder.
    1. With what angle must the apple be thrown?
    2. What must be the initial velocity of the ball?
  1. During a Glen Oak golf tournament, a golfer attempts to take a shortcut to the green by hitting over the trees which are 19.6 m in height when the golf ball is 29.4 m from the woods.
    1. With what vertical velocity component must the ball be hit to enable the ball to just clear the trees?
    2. How long will it take the ball to travel the 29.4 m horizontal distance to the trees?
    3. At what angle must the ball be hit to successfully accomplish this shot?

  63.  Bill kicks a football at an angle of 37° with the horizontal and with an initial speed of 48 ft/sec.  A player from the visiting team, standing 70  yards downfield, starts to run toward Bill the moment the ball is  kicked.  How fast must the player run in order to catch the ball before it hits the ground? 

  64.  A rocket is fired across a gorge toward the cliff 120 ft high and 110 ft away with an instantaneous initial velocity of 175 ft/sec and at an angle of 65° with the horizontal.

             a.   How far above the base of the gorge does the rocket strike the cliff?

             b.  How long is the rocket in the air?

            c.  What is the rocket's striking velocity?

 

  65.  A stone is thrown downward from the top of a building with an instantaneous velocity of 38 m/sec.  The building is 268 m in height and the stone is thrown at an angle of 32° BELOW the horizontal.

            a.    How long is the stone in the air?

            b.  With what velocity does the stone strike the ground below?

            c.    How far horizontally does it travel?

  66.  A morter shell is fired toward the top of a cliff where an emplacement is located.  The cliff is 35 m in height and is located 60 m horizontally from where the mortar is located.  If the mortar round has a muzzle velocity of 145 m/sec and is projected at an angle of 55° with the horizontal:

            a.   Where does the mortar round strike (how far up the cliff if it does not make it to the top, how far back from the front edge of the cliff if it clears the edge)?

            b.   What is the total time in the air?

            c.   What is the velocity with which the round strikes the ground?

 

  67. In attempting to run a cable across a canyon, the telephone company fastens a fine string to an arrow which in turn will be fastened to the cable to pull it across.  The arrow is then projected toward the other side with a velocity of 150 m/sec at an angle of 35° with the horizontal.  If the canyon is 4000 m wide and 80 m deep:

            a.   Will the arrow successfully reach the other side?

            b.   How far downrange will the arrow travel?

            c.   How long will it be in the air?

            d.   With what velocity will it strike?

 

 

 

Multiple Choice Self-Test

 

  1. When an object is thrown horizontally and allowed to fall freely, its velocity,
    1. Is constant and downward.
    2. Is constant and horizontal.
    3. Changes in direction but not in magnitude.
    4. Changes in doth direction and magnitude.

 

  1. A ball is thrown upward at an angle of 60º with the horizontal at 10 m/sec.  Its horizontal velocity will be,
    1. 5 m/sec and steady.
    2. 5 m/sec and decreasing.
    3. 9.8 m/sec and increasing.
    4. 9.8 m/sec and decreasing.
    5. 8.7 m/sec and steady.

 

  1. For the ball in question #2, its vertical velocity will be,
    1. 5 m/sec and decreasing.
    2. 9.8 m/sec and decreasing.
    3. Decreasing at the rate of 9.8 m/sec2.
    4. 8.7 m/sec and steady.

 

  1. The acceleration of a freely falling body during the fifth second is,
    1. 32 ft/sec2
    2. 6.4 ft/sec2
    3. 160 ft/sec2
    4. 400 ft/sec2

 

  1. A package is dropped from an airplane flying horizontally.  The air resistance on the package remains negligible as the plane increases velocity.  The time required for a second package to reach the ground,
    1. Increases
    2. Decreases
    3. Is unchanged
    4. Is unpredictable

 

  1. The velocity with which the hammer of a pile driver will strike the head of a pile after 1.5 seconds of free fall is,
    1. 16 ft/sec
    2. 32 ft/sec
    3. 48 ft/sec
    4. 64 ft/sec

 

  1. If two projectiles experience the same horizontal displacement in the same time interval, they must have the same,
    1. Final velocity
    2. Initial velocity
    3. Acceleration
    4. Average velocity

 

  1. Which of the following is not being accelerated.
    1. A freely falling stone
    2. A satellite in a stable circular orbit
    3. A car moving with constant velocity
    4. A bullet in its trajectory