4 A ball \(A\) is released from rest at the top of a tall tower. One second later, another ball \(B\) is projected vertically upwards from ground level near the bottom of the tower with a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The two balls are at the same height 1.5 s after ball \(B\) is projected.

1. Show that the height of the tower is 50 m .
2. Find the length of time for which ball \(B\) has been in motion when ball \(A\) reaches the ground. Hence find the total distance travelled by ball \(B\) up to the instant when ball \(A\) reaches the ground.