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

According to the problem, for the ball dropped from the building, u₁​=0 and u_2​=40m/s

Velocity of the ball after time t,

v₁​ = u₁ ​− gt

v₁ ​= −gt

And for another ball which is thrown upward,

u₂ ​= 40m/s

Velocity of the ball after time t,

v_2​ = u_2​ − gt = (40 − gt)

Therefore,

Relative velocity of one ball with respect to another ball is,

v₁₂​ = v₁ ​− v₂​ = −gt − [−40 − gt]

v₁₂ ​= v₁ ​− v₂​ = −gt + 40 + gt = 40m/s

Therefore, relative speed is indepent of time.