7. A ball is projected vertically upwards with a speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(A\) which is 1.5 m above the ground. The ball moves freely under gravity until it reaches the ground. The greatest height attained by the ball is 25.6 m above \(A\).
- Show that \(u = 22.4\).
The ball reaches the ground \(T\) seconds after it has been projected from \(A\).
- Find, to 2 decimal places, the value of \(T\).
The ground is soft and the ball sinks 2.5 cm into the ground before coming to rest. The mass of the ball is 0.6 kg . The ground is assumed to exert a constant resistive force of magnitude \(F\) newtons.
- Find, to 3 significant figures, the value of \(F\).
- State one physical factor which could be taken into account to make the model used in this question more realistic.