A-level · Kinematics

Vertical motion under gravityExam-style questions

Why an object moving freely under gravity is just a constant-acceleration problem with a = ±g, how to choose a positive direction and translate "thrown up", "returns", "hits the ground" into suvat values, and why the up-and-down trip makes distance and displacement differ.

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13 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
A small rock is thrown vertically upwards with speed $12.6\ \text{m s}^{-1}$ from a point $A$ at the top of a vertical quarry face. The rock later lands at the point $B$ on the horizontal floor of the quarry, where $B$ is $28$ m vertically below $A$ . The rock does not bounce when it lands.

The rock is modelled as a particle moving freely under gravity.
(a) Find the speed of the rock at the instant it reaches $B$ .

(3 marks)
(b) Find the time taken for the rock to travel from $A$ to $B$ .

(3 marks)
(c) Find the length of time for which the rock is more than $6$ m above the level of $A$ .

(4 marks)
(d) Sketch a speed-time graph for the motion of the rock from the instant it is thrown until the instant it lands at $B$ .

(No further calculations are required.)

(2 marks)
Level 4 · 12 marksTry it
2
A small stone is dropped from a bridge and falls vertically towards the river below.

Before it reaches the river, the stone passes two fixed points, $P$ and $Q$ , with $Q$ below $P$

The speed of the stone is $u\ \text{m s}^{-1}$ as it passes $P$ and $5u\ \text{m s}^{-1}$ as it passes $Q$

The only force acting on the stone is its weight, and the acceleration due to gravity, $g\ \text{m s}^{-2}$ , is constant.
(a) Show that the stone takes $\dfrac{4u}{g}$ seconds to fall from $P$ to $Q$

(2 marks)
(b) The height of $P$ above the surface of the river is $h$ metres.

Show that

$h > \frac{12u^2}{g}$

Fully justify your answer.

(3 marks)
Level 4 · 5 marksTry it
3
In this question use $g = 9.8\ \text{m s}^{-2}$

A fountain in a park has a nozzle at ground level. Water leaves the nozzle with a speed of $8.4\ \text{m s}^{-1}$

A sign beside the fountain states that the water rises to a height of $3.6$ metres above the ground.
(a) Assume that the water leaves the nozzle vertically upwards.
(a) (i) Verify the statement on the sign.

(ii) State two modelling assumptions on which your answer to part (a)(i) depends.

(4 marks)
(b) In fact the water leaves the nozzle at an angle $\theta$ to the vertical, where $0^\circ \le \theta < 20^\circ$

The greatest height above the ground, $h$ metres, that the water reaches satisfies

$k < h \le 3.6$

Find the value of $k$

(4 marks)
Level 4 · 8 marksTry it