Physics 9702 · AS & A Level · Equations of motion

Equations of motion — practice question

A man on top of a wall throws a small ball straight up with velocity $5.6\,\text{m s}^{-1}$. The ball leaves his hand at a height of $3.1\,\text{m}$ above the ground, as shown in Fig. 3.1. Take air resistance to be negligible.
(a)[2]

Show that the ball reaches a highest point of $4.7\,\text{m}$ above the ground.

(b)[2]

The man does not catch the ball as it comes back down. Calculate the time taken for the ball to drop from its maximum height to the ground.

(c)[3]

The ball is released from the man’s hand at time $t = 0$ and lands on the ground at time $t = T$. On Fig. 3.2, sketch a graph to show how the velocity $v$ of the ball varies with time $t$ from $t = 0$ to $t = T$. Numerical values of $v$ and $t$ are not required. Take $v$ to be positive upwards.

(d)[1]

State what the gradient of the graph in (c) represents.

(e(i))[1]

The man now throws a second ball with the same velocity and from the same height as the first ball. The mass of the second ball is greater than that of the first ball. Assume that air resistance is still negligible. For the first and second balls, compare the magnitudes of their accelerations.

(e(ii))[1]

The man now throws a second ball with the same velocity and from the same height as the first ball. The mass of the second ball is greater than that of the first ball. Assume that air resistance is still negligible. For the first and second balls, compare the speeds with which they hit the ground.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies the kinematic equation $v^2 = u^2 + 2as$

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