Browse Projectiles

75 questions at your level

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Horizontal projection

16 questions

LessonNot started
A ball rolls off the 0.80.8 m table at 5 m s−15\ \text{m s}^{-1}. Find how far from the base of the table it lands, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A stone is thrown horizontally at 15 m s−115\ \text{m s}^{-1} from a cliff 2020 m high. Find
(a) the time to land and (b) the horizontal distance travelled, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 34 marksStart
A particle is projected horizontally at 7 m s−17\ \text{m s}^{-1} from a height of 2.52.5 m. Find its speed when it lands, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected horizontally from a height of 1.81.8 m and lands 44 m away. Find the speed of projection, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A package is released from a plane flying horizontally at 100 m s−1100\ \text{m s}^{-1} at a height of 500500 m. Find
(a) the time before it hits the ground and (b) the horizontal distance it travels, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 34 marksStart
A particle is projected horizontally at 12 m s−112\ \text{m s}^{-1} from a height of 3.23.2 m. Find the angle below the horizontal at which it strikes the ground, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is thrown horizontally at 20 m s−120\ \text{m s}^{-1} from the top of a cliff 4545 m high. Find how far from the foot of the cliff it lands, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
The marble leaves the 2.52.5 m shelf horizontally at 88 m s−1^{-1}.

Find how far from the base of the shelf it lands. (3 marks)
●●●●●Level 33 marksStart
A ball is thrown horizontally from a window 4.94.9 m above level ground and lands 1212 m from the base of the building.

Find the speed at which it was thrown. (4 marks)
●●●●●Level 34 marksStart
A stone is thrown horizontally from a bridge 1010 m above a river.

Find the vertical component of its velocity as it hits the water. (4 marks)
●●●●●Level 34 marksStart
A ball is thrown horizontally at 99 m s−1^{-1} from a height of 1010 m.

Find the speed of the ball as it lands, giving your answer in the form k\sqrt{k} and to 3 significant figures. (4 marks)
●●●●●Level 34 marksStart
For the ball in the previous situation (vx=9v_{x} = 9 m s−1^{-1}, vy=14v_{y} = 14 m s−1^{-1} at impact), find the angle below the horizontal at which it strikes the ground. (3 marks)
●●●●●Level 33 marksStart
A particle is projected horizontally at 1212 m s−1^{-1} from the top of a tall building.
(a) Find the time at which its velocity is directed at 45∘45^{\circ} below the horizontal. (3 marks)
(b) Find how far the particle has fallen by this time. (2 marks)
●●●●●Level 35 marksStart
A stone is projected horizontally, with speed 1212 m s⁻¹, from a point OO at the top of a vertical cliff. The point OO is 4545 m above the sea.

The stone is modelled as a particle moving freely under gravity. Take g=9.8g = 9.8 m s⁻².
(a) Find the time taken for the stone to reach the sea, giving your answer to 33 significant figures. (3 marks)
(b) Find the horizontal distance from the foot of the cliff at which the stone enters the sea, giving your answer to 33 significant figures. (2 marks)
(c) Find the speed of the stone as it enters the sea, and the angle its direction of motion then makes with the horizontal. Give each answer to 33 significant figures. (5 marks)
●●●●●Level 310 marksStart

Projection at an angle

44 questions

LessonNot started
A rugby ball is kicked from a point OO on horizontal ground.

The ball is projected with speed 20 m s−120\ \text{m s}^{-1} at an angle α\alpha above the horizontal, where tan⁡α=34\tan\alpha = \frac{3}{4}

The ball is modelled as a particle moving freely under gravity.

Using the model,
(a) find the greatest height of the ball above the ground,

(2 marks)
(b) find the speed of the ball 22 seconds after it is kicked.

(2 marks)
●●●●●Level 34 marksStart
A particle is projected at 30 m s−130\ \text{m s}^{-1} at 40∘40^\circ above the horizontal. Find the greatest height reached, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected at 24 m s−124\ \text{m s}^{-1} at 35∘35^\circ above the horizontal over level ground. Find the time of flight, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A stone is projected at 28 m s−128\ \text{m s}^{-1} at 40∘40^\circ above the horizontal over level ground. Find the horizontal range, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A particle is projected at 20 m s−120\ \text{m s}^{-1} at 50∘50^\circ above the horizontal. Find its speed 1.51.5 s after projection, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected at 30 m s−130\ \text{m s}^{-1} at 45∘45^\circ above the horizontal towards a wall 2020 m away. Find the height at which it strikes the wall, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A particle is projected at 40 m s−140\ \text{m s}^{-1} at 30∘30^\circ above the horizontal. Find
(a) the greatest height and (b) the time taken to reach it, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 34 marksStart
The ball is projected at 2020 m s−1^{-1} at 30∘30^{\circ} above the horizontal.

Find the greatest height reached above the point of projection. (3 marks)
●●●●●Level 33 marksStart
The ball is projected at 2020 m s−1^{-1} at 30∘30^{\circ} above the horizontal over level ground.
(a) Find the total time of flight. (2 marks)
(b) Find the horizontal range. (3 marks)
●●●●●Level 35 marksStart

Projectile motion formulae

41 questions

LessonNot started
A rugby ball is kicked from a point OO on horizontal ground.

The ball is projected with speed 20 m s−120\ \text{m s}^{-1} at an angle α\alpha above the horizontal, where tan⁡α=34\tan\alpha = \frac{3}{4}

The ball is modelled as a particle moving freely under gravity.

Using the model,
(a) find the greatest height of the ball above the ground,

(2 marks)
(b) find the speed of the ball 22 seconds after it is kicked.

(2 marks)
●●●●●Level 34 marksStart
A stone is thrown at 21 m s−121\ \text{m s}^{-1} at 45∘45^\circ over level ground. Use R=u2sin⁡2θgR = \dfrac{u^2\sin 2\theta}{g} to find the range. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected at 30 m s−130\ \text{m s}^{-1} at 30∘30^\circ over level ground. Find the time of flight, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A particle is projected at 24 m s−124\ \text{m s}^{-1} at 60∘60^\circ. Use H=u2sin⁡2θ2gH = \dfrac{u^2\sin^2\theta}{2g} to find the greatest height, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected at 20 m s−120\ \text{m s}^{-1} and lands 3030 m away on level ground. Find the two possible angles of projection, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A projectile is launched at 35 m s−135\ \text{m s}^{-1}. Find the maximum possible range and the angle that achieves it. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected at 25 m s−125\ \text{m s}^{-1} and has a range of 5050 m on level ground. Find the two possible angles of projection, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A ball is projected at 28 m s−128\ \text{m s}^{-1} at 45∘45^\circ. Find its greatest height, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A projectile launched at 30∘30^\circ above the horizontal reaches a greatest height of 1010 m. Find its speed of projection, to 3 s.f. (g=9.8g = 9.8.)
●●●●●Level 32 marksStart
A particle is projected at 2121 m s−1^{-1} at 60∘60^{\circ} above the horizontal.

Use H=u2sin⁡2α2gH = \dfrac{u^{2}\sin^{2}\alpha}{2g} to find the greatest height reached. (3 marks)
●●●●●Level 33 marksStart
A projectile is launched at 4242 m s−1^{-1} over level ground.

Find the maximum possible range, and state the angle of projection that achieves it. (3 marks)
●●●●●Level 33 marksStart
A stone is projected horizontally, with speed 1212 m s⁻¹, from a point OO at the top of a vertical cliff. The point OO is 4545 m above the sea.

The stone is modelled as a particle moving freely under gravity. Take g=9.8g = 9.8 m s⁻².
(a) Find the time taken for the stone to reach the sea, giving your answer to 33 significant figures. (3 marks)
(b) Find the horizontal distance from the foot of the cliff at which the stone enters the sea, giving your answer to 33 significant figures. (2 marks)
(c) Find the speed of the stone as it enters the sea, and the angle its direction of motion then makes with the horizontal. Give each answer to 33 significant figures. (5 marks)
●●●●●Level 310 marksStart