A stone is thrown vertically upwards with speed \(16 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(h\) metres above the ground. The stone hits the ground 4 s later. Find
the value of \(h\),
the speed of the stone as it hits the ground.
(a) Two particles \(A\) and \(B\), of mass 3 kg and 2 kg respectively, are moving in the same direction on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of \(A\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the collision, the particles join to form a single particle \(C\).
Find the speed of \(C\) immediately after the collision.
Two particles \(P\) and \(Q\) have mass 3 kg and \(m \mathrm {~kg}\) respectively. They are moving towards each other in opposite directions on a smooth horizontal table. Each particle has speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), when they collide directly. In this collision, the direction of motion of each particle is reversed. The speed of \(P\) immediately after the collision is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(Q\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
the value of \(m\),
the magnitude of the impulse exerted on \(Q\) in the collision.