Question

The maximum separation between the floor of elevator and the ball during its flight is:

• A. $30m$
• B. $15m$
• C. $7.62m$
• D. $9.5m$

Answer 1

Answer: (C)

$7.62m$

Initial point of floor is considered as reference point.

We have, $x=x_0+ut+\frac{1}{2}{at}^2$

$x_b=2+25t-5t^2$

$x_{ele}=10t+{1/2\times 10t}^2=10t+{5t}^2$

Separation, $\Delta =x_b-x_{ele}$

$\Rightarrow \Delta =2+15t-10t^2$

$\frac{d\Delta }{dt}=0\Rightarrow 15-20t=0$

$\Rightarrow t=\frac{3}{4}$

as $\frac{d^2\Delta }{{dt}^2}<0$, $\Delta$ at $t=\frac{3}{4}$ will be max.

$\therefore$ $\Delta$ at $t=\frac{3}{4}=2+15\times \frac{3}{4}-10\times {\left(\frac{3}{4}\right)}^2$

$=7.625m$