5 A small sphere of mass 0.2 kg is projected vertically downwards with a speed of \(5 \mathrm {~ms} ^ { - 1 }\) from a height of 1.6 m above horizontal ground. It hits the ground and rebounds vertically upwards coming to instantaneous rest at a height of \(h \mathrm {~m}\) above the ground. The coefficient of restitution between the sphere and the ground is 0.7 .

1. Find \(h\).
2. Find the magnitude and direction of the impulse exerted on the sphere by the ground.
3. Find the loss of energy of the sphere between the instant of projection and the instant it comes to instantaneous rest at height \(h \mathrm {~m}\).