Projectiles Cambridge International AS & A Level Physics revision
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In plain words
Throw a ball across a field and it follows a curve. The secret is that its sideways motion and its up-and-down motion have nothing to do with each other. Sideways, nothing pushes it, so it keeps a steady speed. Vertically, gravity acts on it exactly as if it had been dropped.
Three things to know
- Treat the horizontal and vertical motions separately. Horizontally the velocity is constant (no force, ignoring air resistance). Vertically the acceleration is g downwards.
- Split the launch velocity u at angle θ into u cos θ horizontally and u sin θ vertically.
- Find the time from the vertical motion, then use it in the horizontal: range = horizontal velocity × time of flight.
Worked example
A ball is thrown horizontally at 12 m/s from the top of a cliff 45 m high. How far from the foot of the cliff does it land?
- Vertically it starts with no velocity: 45 = ½ × 9.81 × t², so t = 3.03 s.
- Horizontally it keeps moving at 12 m/s for that time.
- Range = 12 × 3.03 = 36 m.
Tips and tricks
- Time is the only thing the two motions share. Find it from one and use it in the other.
- At the highest point the vertical velocity is zero, but the horizontal velocity is unchanged.
It lands in your notebook with its questions as flashcards.
Projectiles: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is true of a projectile at the top of its path?
It is still moving sideways, and still accelerating downwards.
One ball is dropped and another is thrown horizontally from the same height at the same moment. Which lands first?
Their vertical motions are identical.
What is the horizontal component of a velocity of 30 m/s at 60° to the horizontal?
30 cos 60°.
Ignoring air resistance, which launch angle gives the greatest range on level ground?
It gives the best balance of time in the air and horizontal speed.
What is the acceleration of a projectile during its flight?
Gravity is the only force acting.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
Projectiles
Cambridge International AS & A Level Physics 9702 · 8 marks · papermunch.org
Name ______________________________ Date ______________
A projectile is launched at 20 m/s at 30° above the horizontal from level ground. Find its time of flight and its range.[4]
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2.04 s and 35 m. Vertical component 10 m/s: time up = 10 ÷ 9.81 = 1.02 s, so 2.04 s in all. Horizontal component 17.3 m/s × 2.04 s.
For the projectile above, find the maximum height reached.[2]
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5.1 m. 10² ÷ (2 × 9.81).
Explain why the horizontal velocity of a projectile stays constant.[2]
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There is no horizontal force on it (air resistance is ignored), so it has no horizontal acceleration.
Answers: Projectiles
- 1. 2.04 s and 35 m. Vertical component 10 m/s: time up = 10 ÷ 9.81 = 1.02 s, so 2.04 s in all. Horizontal component 17.3 m/s × 2.04 s.
- 2. 5.1 m. 10² ÷ (2 × 9.81).
- 3. There is no horizontal force on it (air resistance is ignored), so it has no horizontal acceleration.