A small ball is projected vertically upwards from a point \(A\). The greatest height reached by the ball is 40 m above \(A\). Calculate
the speed of projection,
the time between the instant that the ball is projected and the instant it returns to \(A\).
A railway truck \(S\) of mass 2000 kg is travelling due east along a straight horizontal track with constant speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The truck \(S\) collides with a truck \(T\) which is travelling due west along the same track as \(S\) with constant speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The magnitude of the impulse of \(T\) on \(S\) is 28800 Ns.
Calculate the speed of \(S\) immediately after the collision.
State the direction of motion of \(S\) immediately after the collision.
Given that, immediately after the collision, the speed of \(T\) is \(3.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and that \(T\) and \(S\) are moving in opposite directions,