A ball is dropped from a building of height 45 m. Simultaneously another ball is thrown up with a speed of 40 m/s. Calculate the relative speed of the balls as a function of time.

Hint: Here relative acceleration of balls with respect to each other is zero.
Step 1: Calculate the velocities of both balls after time t.
 

For the ball dropped from the building, u1=0,u2=40m/s
The velocity of the dropped ball after time t,

v1=u1+gtv1=gt (downward) 

For the ball thrown up, u2 = 40 m/s
The velocity of the ball after time t

v2=u2gt=(40gt) (upward) 

Step 2: Calculate the relative velocity

 The relative velocity of one ball w.r.t. another ball

=v1v2=gt[(40gt)]=40m/s.