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1 Kinematics

Two balls are dropped from the top of a high tower with a time interval t₀ second, where t₀ is smaller than the time taken by the first ball to reach the floor, which is perfectly inelastic. The distance ‘s’ between the two balls, plotted against the time lapse ‘t’ from the instant of dropping the second ball is best represented by –

1) 2)
3) 4)

Option 1

Option 2

Option 3 Solution:

SOLUTION

First ball is in air for time t₀ + t and for it
u = 0, a = g

Second ball is in air for time t and for it
u = 0, a = g

∴ Distance between balls at time t

The equation for s is linear in t (y = mx + c), so graph of s versus t is a straight line.
After ball 1 reaches the ground it stays there
Hence, distance between balls =1/2gt²

s =g/2 t² (parabola opening upwards).

Option 4

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