Ceist Eile

Ceist Eile is in development. Features, questions and prices may change while we refine it.

Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Oblique collisions

How often Oblique collisions 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

Oblique collisions, Higher Level(7 marks)

Quick ones on Oblique collisions.

(a)Smooth spheres collide obliquely. Which velocity component of each sphere is unchanged?
  1. Parallel to the line of centres
  2. Perpendicular to the line of centres
  3. Neither component; both change
(b)In an oblique collision, along which line are PCM and NEL applied?
  1. The direction the moving sphere was travelling
  2. The line perpendicular to the line of centres
  3. The line of centres
(c)Why is the j-component unchanged in an oblique collision of smooth spheres (i along the line of centres)?
  1. The impulse acts only along the line of centres
  2. e is zero along the j-direction, so nothing changes
  3. Momentum is not conserved along the j-direction
Show the answers

(a) Perpendicular to the line of centres

(b) The line of centres

(c) The impulse acts only along the line of centres

Your turn: Higher Level questions on Oblique collisions.

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
2025Q9
2024Q3
2023Q2

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

More Oblique collisions questions

Oblique collisions, 3 marks

A (1 kg, 6i + 3j m/s) hits B (2 kg) at rest; line of centres along i, e = ½. A's velocity after?

  1. 2i + 3j m/s
  2. −2i + 3j m/s
  3. 3j m/s
Show the answer

3j m/s

Along i: PCM v₁ + 2v₂ = 6, NEL v₂ − v₁ = 3. So 3v₁ = 0, v₁ = 0 and v₂ = 3. A keeps its j-part, so it moves off at 3j. 2i + 3j is the e = 0 answer.

Oblique collisions, 3 marks

A ball hits a smooth wall at 45° to it, with e = ⅓. tan of the angle between its rebound path and the wall?

  1. 1
  2. ⅓
  3. 3
Show the answer

⅓

At 45° the parts along and into the wall are equal, say a. After impact the part along the wall is still a, the part away from it is a/3, so tan = (a/3) ÷ a = ⅓.

Oblique collisions, 2 marks

Smooth spheres collide obliquely with e = 1. Kinetic energy lost?

  1. None
  2. Half of it
  3. It depends on the angle of impact
Show the answer

None

e = 1 is a perfectly elastic impact: the speed of separation along the line of centres equals the speed of approach, so no KE is lost. The j-parts never lose any.

Other Applied Maths topics

All of Leaving Cert Applied Maths