Two balls are thrown up simultaneously from the top of a `400 m` high tower with speed `10 m//`s and `55 m//s`. Sketch a graph showing the separation between the balls versus time.

Explanation

Taking O as the origin,

displacement of ball(1), `s_(1)=400+10t-1/2 g t^(2)`
Displacement of ball (2), `s_(2)=400+55t-1/2 g t^(2)`
Sepration between balls `s=s_(2)-s_(1)=45 t`
The first ball strikes the ground.
`s_(1)=0=400+10t-1/2 g t^(2)=400+10 t-5 t^(2)`
`t^(2)-2t+80=0`
`(t-10)(t+8)=0impliest=10s,-8 s`
Time cannot be negative, so `t=10 s`.
The second ball strikes the ground.
`s_(2)=0=400+55 t-1/2 g t^(2)=400+55 t-5 t^(2)`
`t^(2)-11t+80=0`
`(t-16)(t+5)=0 implies t=16s`
from `t=0` to `t=10 s`, `s=s_(2)-s_(1)=45t`
Shape: `y=45x` (inclined straight line with +ve slope)
From `t= 10` to `16 s, s=s_(2)-0=400+55t-5 t^(2)`
Shape:`y=400+55x-5x^(2)` (parabola, open downward)