A-level · Projectiles

Projection at an angleExam-style questions

Resolving the launch velocity into u cosθ (horizontal, constant) and u sinθ (vertical, under gravity), then using suvat in each direction to find the time of flight, greatest height and range.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A ball is projected at $35\ \text{m s}^{-1}$ at $25^\circ$ above the horizontal over level ground.
(a) Find the time of flight.
(b) Find the horizontal range. Give answers to 3 s.f. ( $g = 9.8$ .)
Level 5 · 4 marksTry it
2
A stone is projected at $25$ m s $^{-1}$ at $40^{\circ}$ above the horizontal.

Find the speed and direction of motion of the stone $2$ seconds after projection. (6 marks)
Level 5 · 6 marksTry it
3
A ball is kicked from level ground at $22$ m s $^{-1}$ at $35^{\circ}$ above the horizontal, directly towards a wall $15$ m away. The wall is $3$ m tall.

Determine whether the ball clears the wall, and by what vertical margin. (5 marks)
Level 5 · 5 marksTry it
4
A ball is kicked from a point $O$ on horizontal ground with speed $14$ m s⁻¹ at an angle $\theta$ above the horizontal, where $0 < \theta < 90^\circ$ . The ball is modelled as a particle moving freely under gravity. Take $g = 9.8$ m s⁻².

After $t$ seconds the horizontal and vertical displacements of the ball from $O$ are $x$ metres and $y$ metres respectively.
(a) Show that $y = x\tan\theta - \dfrac{x^2}{40}\left(1 + \tan^2\theta\right)$ . (3 marks)

The ball passes through the point $P$ , which is $10$ m horizontally from $O$ and $5$ m above the ground.
(b) Show that $\tan^2\theta - 4\tan\theta + 3 = 0$ , and hence find the two possible values of $\theta$ . (4 marks)
(c) Show that, for either value of $\theta$ , the speed of the ball as it passes through $P$ is $7\sqrt{2}$ m s⁻¹. (3 marks)
(d) For the smaller value of $\theta$ , determine whether the ball is rising, falling or at its highest point as it passes through $P$ . Fully justify your answer. (2 marks)
Level 5 · 12 marksTry it
5
A stone is thrown from a point $O$ at the top of a vertical cliff, $25$ m above horizontal ground. It is thrown with speed $15$ m s⁻¹ at an angle of $30^\circ$ above the horizontal.

The stone is modelled as a particle moving freely under gravity. Take $g = 9.8$ m s⁻².
(a) Find the time taken for the stone to reach the ground, giving your answer to $3$ significant figures. (5 marks)
(b) Find the horizontal distance from the foot of the cliff at which the stone lands, giving your answer to $3$ significant figures. (2 marks)
(c) Find the speed of the stone as it hits the ground, giving your answer to $3$ significant figures. (3 marks)
(d) Find the greatest height above the ground reached by the stone, giving your answer to $3$ significant figures. (2 marks)
Level 5 · 12 marksTry it

8 more questions on projection at an angle

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free