Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speeds of 10 m/s and 40 m/s respectively. Which of the following graphs best represents the time variation of relative position of the second stone with respect to the first?
(Assume stones do not rebound after hitting the ground and neglect air resistance take g = 10 `m//s^(2)` ) The figures are schematic and not drawn to scale)

Options

A.
B.
C.
D.

Answer

C

Explanation

We consider the upward direction to be positive.
`:. Y = ut -(1)/(2)"gt"^(2)`
Till they reach the ground for the first stone,
`-240 = 10t- (1)/(2)xx10t^(2)`
or, `5t^(2)-10t-240 =0 " ""or", 5(t+6)(t-8)=0`
`:.` t = 12s
So, for the last (12-8=) 4s, only the second stone will be in motion. Hence in the time span between 8 s and 12s
`y_(2)-y_(1)=(40t-5t^(2))-0=40t-5t^(2)`
which is the equation of a parabola.
Now in the time span between 0 s to 8 s , ` y_(2)-y_(1)= (40t-5t^(2))-(10t-5t^(2)) = 30t`
which is the equation of a straight line passing through the origin.