Question

A vertical tower is 100m high. From the top of tower, a ball A is dropped. Simultaneously a second ball B is projected vertically upwards from ground with a speed of 40 ms^-1. Where and when the two balls cross one another? What is instanteous velocitiy of the each ball at this moment of time? g = 10ms^-2

Answer 1

In Fig.(a) O is point an ground and O1 is the top of tower. Choose O as origin and vertically upward direction as positive z–axis. For ball A;

For ball A;

For ball B,

When the two balls cross one another, their instantaneous position co-ordinate is same, i.e. z_A = z_B . From Eqns. (i) and (ii)

100 – 5t² = 40t–5t² 

or t = 2.5s

The two balls cross one another 2.5s after projection. The instantaneous position co-ordinate of a from Eqn. (i) is

z_A = 100-5 (2.5)² = 68.75 m

The two balls cross one another at a point 68.75m above ground. Let v_A and v_B be their instantaneous velocity. Obviously

Negative sign of v_A indicates that ball A is moving vertically downwards. The positive sign of v_B indicates that ball B is moving vertically upwards. This is shown in Fig(b).