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Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Projectile motion

How often Projectile motion comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

OL Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Projectile motion, Higher Level(7 marks)

Quick ones on Projectile motion.

(a)A ball is projected at 14i + 19.6j m/s from level ground (g = 9.8). Time of flight?
  1. 2 s
  2. 4 s
  3. 1.43 s
(b)At the highest point of its flight, a projectile's velocity is…?
  1. Vertical, equal to u sin α
  2. Zero
  3. Horizontal, equal to u cos α
(c)Time for a projectile (speed u, angle α) to reach its maximum height?
  1. u sin α / g
  2. u cos α / g
  3. 2u sin α / g
Show the answers

(a) 4 s

(b) Horizontal, equal to u cos α

(c) u sin α / g

Your turn: Higher Level questions on Projectile motion.

Higher Level

Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q7, Q10
2024Q7
2023Q3, Q8

Links open the State Examinations Commission’s paper for that year.

More Projectile motion questions

Projectile motion, 3 marks

A ball hits a smooth vertical wall (perpendicular to i) with velocity 12i − 5j m/s, e = 0.5. Velocity just after?

  1. −6i + 2.5j m/s
  2. −12i − 5j m/s
  3. −6i − 5j m/s
Show the answer

−6i − 5j m/s

Only the component into the wall changes: it reverses and is multiplied by e, giving −6i. The j-component along the smooth wall is unchanged at −5j.

Projectile motion, 3 marks

A projectile's height is y = 19.6t − 4.9t² (g = 9.8). When is it 14.7 m high?

  1. t = 1 s only
  2. t = 1 s and t = 3 s
  3. t = 2 s only
Show the answer

t = 1 s and t = 3 s

4.9t² − 19.6t + 14.7 = 0 becomes t² − 4t + 3 = 0, so (t − 1)(t − 3) = 0. Once on the way up and once on the way down; t = 2 is the top.

Projectile motion, 2 marks

With no air resistance, what happens to a projectile's horizontal velocity during flight?

  1. It stays constant
  2. It decreases steadily
  3. It increases steadily
Show the answer

It stays constant

Gravity acts only vertically, so no force acts horizontally. The i-component u cos α stays the same from launch to landing; only the j-component changes.

Ordinary Level

Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q6
2024Q4
2023Q5

Links open the State Examinations Commission’s paper for that year.

More Projectile motion questions

Projectile motion, 2 marks

With no air resistance, the vertical acceleration of a projectile is…

  1. 0 m s⁻²
  2. 9.8 m s⁻² upwards
  3. 9.8 m s⁻² downwards
Show the answer

9.8 m s⁻² downwards

The only force is the weight, so the acceleration is g = 9.8 m s⁻² down, on the way up and on the way down.

Projectile motion, 3 marks

A ball is thrown horizontally at 10 m s⁻¹ from a cliff. Horizontal distance after 3 s?

  1. 3.3 m
  2. 30 m
  3. 44.1 m
Show the answer

30 m

Horizontal velocity stays at 10 m s⁻¹, so distance = 10 × 3 = 30 m. 44.1 m is how far it has fallen vertically in 3 s.

Projectile motion, 3 marks

A projectile has u = 14i + 19.6j m s⁻¹. Time to maximum height? (g = 9.8 m s⁻²)

  1. 2 s
  2. 4 s
  3. 1.43 s
Show the answer

2 s

At the top the vertical velocity is 0: 0 = 19.6 − 9.8t, so t = 2 s. Only the j part matters; 1.43 wrongly uses the 14.

Other Applied Maths topics

All of Leaving Cert Applied Maths