Further Maths M1 Easter 2025

A particle P of mass 3 kg is moving with a speed of 8 ms-1 in a straight horizontal line when it collides with particle Q, of mass 4 kg, which is moving in the opposite direction with speed 1.5 ms^-1 . After the collision, the direction of motion of P is unchanged and it moves with a speed of 2 ms^-1 . The direction of motion of Q is reversed. Find the speed of Q after the collision.

• 6 ms^-1

• 3 ms^-1

• 4 ms^-1

• 4.5 ms^-1

An ice hockey puck, of mass 0.2 kg, is moving along smooth horizontal ice with a speed of 10 ms^–1 when it receives a direct hit from a stick which reverses its direction and increases its speed to 15 ms^–1. Calculate the magnitude of the impulse exerted by the stick on the puck.

• 1 Ns

• 10 Ns

• 5 Ns

• 25 Ns

A particle A of mass 4 kg is moving with velocity (3i + 5j) ms^–1 on horizontal ground when it collides with a second particle B, with mass 2 kg, which is moving with velocity (–2i + 4j) ms^–1 . As a result of the collision, B is brought to rest. Find the speed of A after the collision.

• 7.23 ms^-1

• 8.06 ms^-1

• (2 𝒊 + 7j) ms^-1

• 29.1 ms^-1

A particle A of mass 4 kg is moving with velocity (3i + 5j) ms^–1 on horizontal ground when it collides with a second particle B, with mass 2 kg, which is moving with velocity (–2i + 4j) ms^–1 . As a result of the collision, B is brought to rest. Find the direction of A after the collision.

Particle P has mass 3 kg and particle Q has mass m kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of P is 4 ms^-1 and the speed of Q is 3 ms^-1 . In the collision the direction of motion of P is unchanged and the direction of motion is Q is reversed. Immediately after the collision, the speed of P is 1 ms^-1 and the speed of Q is 1.5 ms^-1 . Find the magnitude of the impulse exerted on P in the collision.

• 9 NS

• 12 NS

• 8 Ns

• 15 Ns

Particle P has mass 3 kg and particle Q has mass m kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of P is 4 ms^-1 and the speed of Q is 3 ms^-1 . In the collision the direction of motion of P is unchanged and the direction of motion is Q is reversed. Immediately after the collision, the speed of P is 1 ms^-1 and the speed of Q is 1.5 ms^-1 . Find the value of m.

• 4.5

• 3

• 2

• 4

• 2u

• 15u

• u

• 5u

Two particles P and Q have masses 4m and m respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of P and Q immediately before the collision are 2u and 5u respectively. Immediately after the collision, the speed of P is 12𝑢 and its direction of motion is reversed. Find the Two particles P and Q have masses 4m and m respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of P and Q immediately before the collision are 2u and 5u respectively. Immediately after the collision, the speed of P is 1 2 𝑢 and its direction of motion is reversed. Find the speed and direction of Q after the collision.

• 2u in the same direction

• 5u in the

  opposite direction

• u in the opposite direction

• 5u in the same direction

Two particles P and Q have masses 4m and m respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of P and Q immediately before the collision are 2u and 5u respectively. Immediately after the collision, the speed of P is 12𝑢 and its direction of motion is reversed. Find the Two particles P and Q have masses 4m and m respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of P and Q immediately before the collision are 2u and 5u respectively. Immediately after the collision, the speed of P is 1 2 𝑢 and its direction of motion is reversed. Find the magnitude of the impulse exerted on P by Q in the collision.

• 10mu

• 0

• 5mu

• 2mu

A tennis ball of mass 0.1 kg is hit by a racquet. Immediately before being hit, the ball has a velocity 30 i ms^-1. The racquet exerts an impulse of (-2i – 4j) Ns on the ball. By modelling the ball as a particle, find the velocity of the ball immediately after being hit.

• (10 i – 40j) ms^-1

• (10 i + 40j) ms^-1

• 41.2 ms^-1

• (-10 i + 40j) ms^-1