1 A smooth sphere of mass 0.3 kg bounces on a fixed horizontal surface. Immediately before the sphere bounces the components of its velocity horizontally and vertically downwards are \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. The speed of the sphere immediately after it bounces is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that the vertical component of the velocity of the sphere immediately after impact is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and hence find the coefficient of restitution between the surface and the sphere.
2. State the direction of the impulse on the sphere and find its magnitude.