5. In a "test your strength" game at an amusement park, competitors hit one end of a small lever with a hammer, causing the other end of the lever to strike a ball which then moves in a vertical tube whose total height is adjustable. The ball is attached to one end of an elastic spring of natural length 3 m and modulus of elasticity 120 N . The mass of the ball is 2 kg . The other end of the spring is attached to the top of the tube. The ball is modelled as a particle, the spring as light and the tube is assumed to be smooth. The height of the tube is first set at 3 m . A competitor gives the ball an initial speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find the height to which the ball rises before coming to rest. The tube is now adjusted by reducing its height to 2.5 m . The spring and the ball remain unchanged.
2. Find the initial speed which the ball must now have if it is to rise by the same distance as in part (a).
   (5 marks)