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

Options

A. .
B. .
C. .
D. .

Answer

C

Explanation

For the second stone time required to reach the ground is given by `y = ut - (1)/(2) g t^2`
`- 240 = 40 t - (1)/(2) xx 10 xx t^2`
:. `5t^2 - 40 t - 240 = 0`
`(t - 12)(t + 8) = 0`
:. `t = 12 s`
For the first stone : `- 240 = 10 t - (1)/(2) xx 10 xx t^2`
:. `- 240 = 10t - 5t^2`
`5 t^2 - 10 t - 240 = 0`
`(t - 8)(t + 6) = 0`
`T = 8 s `
During first `8` seconds both stones are in are :
:. `y_2 - y_1 = (u_2 - u_1) t = 30 t`
So, graph of `(y_2 - y_1)` against `t` is a straight line.
After `8` seconds.
`y_2 = u_2 t - (1)/(2) g t^2 - 240`
Stones two has acceleration with respect to stone one. Hence graph (c ) is the correct description.