## Impulses in Two Dimensions

Impulse in a vector. An object may experience an impulse acting at any angle to it's path, forcing it to change direction by any angle. We should always represent impulse by a vector. This may be strictly unnecessary if the impulse acts along the path of the velocity, but it becomes essential if the impulse does not act along the path of the velocity.

We can use the equation where and are all vectors.

We can use this equation to find any of given the other three.

It should also be noted that

1. If in a collision a particle experiences an impulse the other particle experiences an impulse of This is Newton's 3rd Law – To every action there is an equal and opposite reaction.

2. In general collisions result in a loss of kinetic energy: - individual kinetic energies may increase, but the overall kinetic energy may not. Only in perfectly elastic collisions is kinetic energy conserved.

Example

A ball has mass 0.2 kg. It is moving with velocity when it is struck by a bat. The bat

exerts an impulse of on the ball.

Find

a) the velocity of the ball immediately after the impact,.

b) the angle through which the ball is deflected as a result of the impact.

c) the kinetic energy lost by the ball in the impact.   b) c) 