6 A ball of mass 0.15 kg is hit directly by a vertical cricket bat. Immediately before the impact, the ball is travelling horizontally with speed \(28 \mathrm {~ms} ^ { - 1 }\) Immediately after the impact, the ball is travelling horizontally with speed \(14 \mathrm {~ms} ^ { - 1 }\) in the opposite direction. 6

1. Find the magnitude of the impulse exerted by the bat on the ball.
   [0pt] [2 marks]
   6
2. In a simple model the force, \(F\) newtons, exerted by the bat on the ball, \(t\) seconds after the initial impact, is given by $$F = 10 k t ( 0.05 - t )$$ where \(k\) is a constant.
   Given the ball is in contact with the bat for 0.05 seconds, find the value of \(k\)
   [0pt] [3 marks]
   \(7 \quad\) Use \(g\) as \(9.81 \mathrm {~ms} ^ { - 2 }\) in this question. A light elastic string has one end attached to a fixed point \(A\) on a smooth plane inclined at \(25 ^ { \circ }\) to the horizontal. The other end of the string is attached to a wooden block of mass 2.5 kg , which rests on the plane. The elastic string has natural length 3 metres and modulus of elasticity 125 newtons.
   The block is pulled down the line of greatest slope of the plane to a point 4.5 metres from \(A\) and then released.