Momentum & Impulse (Edexcel A Level Further Maths: Further Mechanics 1)

A small ball of mass 0.3 kg is released from rest from a point 3.6 m above horizontal ground.
The ball falls freely under gravity, hits the ground and rebounds vertically upwards.

In the first impact with the ground, the ball receives an impulse of magnitude 4.2 Ns.
The ball is modelled as a particle.

Find the speed of the ball immediately after it first hits the ground.

Find the kinetic energy lost by the ball as a result of the impact with the ground.

A particle P, of mass 0.5 kg, is moving with velocity when it receives an impulse  of magnitude 2.5 Ns.

As a result of the impulse, the direction of motion of P is deflected through an angle of 45°.

Given that  Ns, find all the possible pairs of values of and . 

A particle of mass 0.5 kg is moving with velocity  when it receives an impulse  Ns. Immediately after receiving the impulse, is moving with velocity . 

Find the magnitude of .

The angle between the direction of the impulse and the direction of motion of immediately before receiving the impulse is .

Find the value of .

A particle  has mass 0.5 kg. It is moving in the  plane with velocity  when it receives an impulse , where  is a positive constant.

The angle between the direction of motion of immediately before receiving the impulse and the direction of motion of immediately after receiving the impulse is 

Immediately after receiving the impulse, is moving with speed .

Find

the value of  

the value of