Physics 9702 · AS & A Level · Momentum and Newton's laws of motion

Momentum and Newton's laws of motion — practice question

A ball is projected vertically downward to the ground from a height of $1.5\,\text{m}$, and it arrives at the ground with speed $8.7\,\text{m s}^{-1}$. Take air resistance to be negligible.
(a)[2]

Calculate the speed $u$.

(b)[2]

State how Newton’s third law is shown in the collision between the ball and the ground.

(c(i))[2]

The ball is in contact with the ground for $0.091\,\text{s}$. It rebounds vertically and leaves the ground at a speed of $5.4\,\text{m s}^{-1}$. The ball has a mass of $0.059\,\text{kg}$. Calculate the magnitude of the change in momentum of the ball during the collision.

(c(ii))[1]

Determine the magnitude of the average resultant force acting on the ball during the collision.

(c(iii))[2]

Use your answer in (c)(ii) to calculate the magnitude of the average force exerted by the ground on the ball during the collision.

(d)[1]

The ball was thrown downward at time $t = 0$ and reaches the ground at time $t = T$. On Fig. 2.2, sketch a graph to show how the speed of the ball varies with time $t$ from $t = 0$ to $t = T$. Numerical values are not needed.

(e)[2]

In practice, air resistance is not negligible. State and explain the variation, if any, with time $t$ of the gradient of the graph in (d) when air resistance is not negligible.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: $v^2=u^2+2as$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI