4. Andrew hits a tennis ball vertically upwards towards his sister Barbara who is leaning out of a window 7.5 m above the ground to try to catch it. When the ball leaves Andrew's racket, it is 1.9 m above the ground and travelling at \(21 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Barbara fails to catch the ball on its way up but succeeds as the ball comes back down.
Modelling the ball as a particle and assuming that air resistance can be neglected,
- find the maximum height above the ground which the ball reaches.
- find how long Barbara has to wait from the moment that the ball first passes her until she catches it.