Physics 9702 · AS & A Level · Progressive waves

Progressive waves — practice question

As illustrated in Fig. 1.1, a child kicks a ball off level ground with speed $28\,\text{m s}^{-1}$ at an angle of $34^{\circ}$ above the horizontal. Air resistance may be ignored. The ball starts from the ground at time $t = 0$.
(a(i))[2]

Calculate the horizontal component $v_H$ and the vertical component $v_V$ of the ball’s velocity just after it leaves the ground.

(a(ii))[1]

Show that the ball is at its maximum height when $t = 1.6\,\text{s}$.

(a(iii))[1]

On Fig. 1.2, sketch how $v_H$ varies with time $t$ from $t=0$ to $t=3.2\,\text{s}$. Take the upward direction as positive for velocity. Label the line H.

(a(iv))[3]

On Fig. 1.2, sketch the variation of $v_V$ with time $t$ from $t=0$ to $t=3.2\,\text{s}$. Assume that upward velocity is positive. Label your line V.

(b(i))[1]

The ball’s total change in momentum from leaving the ground at $t=0$ to landing on the ground at $t=3.2\,\text{s}$ is $13\,\text{kg m s}^{-1}$. Define momentum.

(b(ii))[2]

Calculate the force acting on the ball while it is in the air.

(b(iii))[1]

Determine the ball’s mass.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence $v_H = 28 \times \cos 34^\circ = 23\ \mathrm{m\ s^{-1}}$

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