Projectile motion and resistive forcesAQA A-Level Physics: Subtopic test

1. 1
   A stone is thrown horizontally at 12 m s⁻¹ from the top of a vertical cliff that is 45 m above the sea. Ignore air resistance and take g = 9.81 m s⁻².

   (a)

   How long does the stone take to reach the sea?

   [1 mark]

   • A3.0 s
   • B4.6 s
   • C9.2 s
   • D1.5 s

   (b)

   How far from the base of the cliff does the stone land?

   [1 mark]

   • A12 m
   • B18 m
   • C36 m
   • D55 m

   (c)

   Calculate the speed of the stone as it reaches the sea.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A football is kicked from level ground with a speed of 20 m s⁻¹ at 35° above the horizontal. Ignore air resistance and take g = 9.81 m s⁻².

   (a)

   What is the initial vertical component of the ball's velocity?

   [1 mark]

   • A16.4 m s⁻¹
   • B11.5 m s⁻¹
   • C20 m s⁻¹
   • D9.81 m s⁻¹

   (b)

   What is the horizontal distance travelled by the ball before it lands?

   [1 mark]

   • A19 m
   • B27 m
   • C33 m
   • D38 m

   (c)

   Explain why the speed of the ball is a minimum at the highest point of its flight.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A skydiver of mass 80 kg jumps from a stationary balloon and falls vertically. Her speed increases at first and she eventually reaches a constant terminal speed. Take g = 9.81 m s⁻².

   (a)

   Explain, in terms of the forces on the skydiver, why her acceleration decreases and she reaches a terminal speed.

   [3 marks]

   (b)

   Calculate the air resistance on the skydiver at terminal speed and her acceleration at the instant she leaves the balloon. She later opens a parachute; describe how her speed changes afterwards.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Moving objects are slowed by resistive forces. A cricket ball is hit through the air and a car travels along a straight level road. In each case air resistance has an important effect on the motion.

   (a)

   The cricket ball is hit from the ground at 40° above the horizontal. Describe and explain how its trajectory differs from that predicted when air resistance is ignored.

   [6 marks]

   (b)

   The car has a mass of 1200 kg. Its engine gives a constant driving force of 1500 N and the rolling friction is a constant 200 N. At a speed of 20 m s⁻¹ the air resistance is 400 N. Explain why the car has a maximum speed, calculate its acceleration at 20 m s⁻¹ and the air resistance at its maximum speed, and explain how streamlining the car would change the maximum speed.

   [6 marks]

   Total for question 4: 12 marks

End of questions