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### Transcript of Projectile Motion - BHS · PDF fileProjectile Motion 11.7 Exercises 1 A ball is thrown...

• Projectile Motion

11.7 Exercises

1 A ball is thrown horizontally from a cliff with a speed of 10ms-I, at the same time as an identical ball is dropped from the cliff. Neglecting the effect of air resistance and taking gravitational acceleration to be g = +9-8m~-~, sketch graphs (on the axes below) to show

(1) the horizontal speed v, of the projected ball versus time, for the duration of its flighi;

(2) the vertical velocity v,, of the projected and dropped balls vs. time, for the duration of its flight.

On the same axes, sketch graphs to show the horizontal speed and the vertical velocity versus time if air resistance has a significant effect on the flight of the ball. Label each graph clearly to distinguish it from the previous graph.

2 On each of the two projectile trajectories depicted below, draw vectors to show the directions and relative magnitudes of the velocity and the acceleration of the projectile at each of the points A, B & C.

3 (1) If a ball is dropped near the surface_ of the Earth, how long will it take to fall 0.7m?

(2) A tennis player hits a ball horizontally at 35ms-l, when it is 1.6m above the ground. If the ball is hit 1 1-Om from the net will the ball clear the net which is 0-9m high?

• 10 Physics Essentials Stage 2 Physics

The multiple image photograph on the right shows the motion of two balls that are released at the same time fiom the point 0. Ball A falls freely while ball B is projected horizontally.

(1) Using measurements fiom the diagram, explain how it shows that the horizontal velocity of B remains constant.

(2) Explain how we can use the photograph to deduce that the velocity of ball A increases during its fall.

..---".-"-"-.- --- "-- ---

(3) Explain why ball B has no acceleration in the horizontal direction.

(4) Ball A is falling freely and has a vertical acceleration g = 9 4 r n ~ - ~ . Using the photograph determine the vertical acceleration of ball B. Explain how you got your answer from the photo.

( 5 ) Which ball will hit the ground with the greater speed? Explain your answer.

• Projectile Motion

5 (1) An object is dropped from a height of 120m above the Earth.

(a) Find its velocity two seconds after it was dropped.

(b) Find the time taken for it to hit the ground.

(2) A parcel is to be dropped from an aeroplane to a boat at sea. The aeroplane is flying with a speed of looms-' at a fixed altitude of 120m above sea level.

(a) What is the vertical velocity of the parcel after two seconds?

(b) Determine the velocity of the parcel after two seconds.

(c) Explain what happens to the two components of the velocity of the parcel as it falls to the water?

(d) How long, from the moment that it is released, does it take for the parcel to hit the water.

(e) How far, before the aeroplane passes over the boat, from the boat must the parcel be released so that it lands in the water near the boat?

• 12 Physics Essentials Stage 2 Physics

6 At a point on the upward path of a projectile the velocity of the projectile is 18ms-I at 40" above the horizontal, as shown in the diagram.

(1) Find the horizontal and vertical components of the velocity at this point.

(2) Describe how (and explain why) these components of velocity will change over the rest of the flight.

- --

(3) What is the velocity of the projectile at point X?

7 (1) An object is dropped from a height of 2m above the ground. Find the time that it will take for this body to hit the ground.

-"-" " " -.--- "" "- " ................... " - ........ " ......

(2) A gun, aimed horizontally, fires a bullet with a speed of 900ms". The gun is 2m above ground level.

(a) What is the time of flight of this bullet? Explain your answer.

(b) Find the range of the bullet.

• Projectile Motion

(c) Find the velocity with which the bullet hits the ground.

8 A mortar shell is fired from ground level (at point A on the diagram) with a velocity vo = looms-' at an angle of 80' above the horizontal.

(1) Calculate the horizontal and vertical components of the velocity of the shell at the instant it is fired.

(2) Calculate the vertical component of the velocity (i) one second and (ii) thirteen seconds after firing.

(ii)

(3) Calculate the resultant velocity of the shell after 13 seconds.

(4) What is the velocity of the shell at point R?

( 5 ) What is the acceleration of the shell at point B?

• Physics Essentials Stage 2 Phvsics

9 (1) An object is dropped from a height of 40m above the surface of the Earth. Calculate long it takes before the object hits the ground?

(2) A stone of mass 200g is thrown with a velocity of vo = 30ms-I horizontally from the observation deck of a lighthouse. At the moment of release the stone is 40m above sea level.

(a) How long does it take before the stone hits the water?

(b) What is the vertical velocity of the stone on impact with the water?

(c) What is the velocity of the stone on impact with the water?

.. .... .----- -- .... " - " " - " ........................

(d) How far does the stone travel horizontally from the point of projection before it hits the water?

(e) Find the total energy (gravitational potential energy and kinetic energy) of the stone at the moment of projection and show that energy is conserved during its flight.

• Prdecfile Motion

10 A golfer hits a ball from an elevated tee, at a height of 20m above the green. The ball is hit

..................................................... with a velocity of 50ms-' at an angle of 20' to the horizontal, and its time of flight before it hits the green is 4-41s.

Find the horizontal and components

of the initial velocity.

................... " .... " .................. " ...................... " ....... " ...... " " ........ - "" " "

(2) Find the time that the ball is in the air before it reaches point B, which is at the same height as the tee.

---

(3) Find the distance that the ball travels horizontally before it hits the green.

-

(4) Find the velocity of the ball when it hits the green.

(5) Explain why the kinetic energy of the ball at impact with the green is greater than it is at the instant when it is hit by the golf club.

• 16 Physics Essentials Stage 2 Physics

11 Water leaves a hose at a speed of va = 2.0ms-', at an angle of 45' above the horizontal. The nozzle is 1 -2m above ground level. The time interval from when the water leaves the nozzle to when A ~r hits the ground is 2.96s.

4 0 . . .. . .. , .. . .. . ... .. . 1 .. . .. .. . . . .. (1) Determine the horizontal distance from the nozzle to the

point where the water hits the ground.

(2) Determine the velocity and the kinetic energy of 1 gram of water at the maximum height.

(3) At which point on the flight path will the speed of the water be the same as the initial speed?

---

(4) The kinetic energy of the water when it hits the ground is greater than when it leaves the nozzle. Explain why this is so and calculate the increase in kinetic energy of one kilogram of water.

(5) What will be the effect on the range if the angle between the nozzle and the horizontal is slightly increased? Explain your answer.

(6) What will be the effect on the range if the angle between the nozzle and the horizontal is slightly decreased? Explain your answer.

• Prdectile Motion

12 A cannonball is fixed at an angle of 45" to the horizontal, thus achieving its maximum range of 5297m on horizontal ground. The cannon ball has a flight time of 32-88s. Assume that the cannonball is projected from ground level.

1 5297m (1) Find the horizontal component 7

of the velocity of the cannon ball during its flight.

............... " .......... " - ........... ...... ............................ " - ............ " " "." ............. """ . " ....--.... " ................................................ .......... " ...........................................

(2) Find the initial velocity of the cannonball.

-

(3) What is the initial vertical velocity of the cannonball?

(4) What is the speed of the cannonball at the top of its flight path?

........................................... ..................................... ......... -.- ......................... --..- ......................

(5) Find the time taken for the cannonball to reach its maximum height.

( 6 ) In another identical firing of this cannon, the cannonball encounters a horizontal headwind (i.e. there is no effect on its vertical velocity, only the horizontal speed is reduced). Explain what effect this wind will have on (i) the time of flight and (ii) the range of the cannonball.

• 1 8 Physics Essentials Stage 2 Physics

13 In an investigation into projectile motion, students projected a golf ball from ground level with the same initial speed but at different angles to the horizontal. At their 'rst attempt the ball was projected at 45" to the horizontal and the range was noted. In subsequent attempts, the angle of projection was progressively increased. Explain what effect (if any) increasing the angle of projection has on

(1) the ball's time of flight.

- -- -

(2) the horizontal component of the ball's initial velocity.

. .. -- ---------------.- ---.- (3) the range of the ball.

14 An athlete, competing in a shot put event, throws a shot of mass 6.0kg with an initial speed of 13111s-' at an angle of 40" to the horizontal. The shot is released at a he