Question

A stone is thrown vertically upwards from the top of a tower $64m$ high according to the law $s=48t-16t^2$. The greatest height attained by the stone above ground is

• A. $36m$
• B. $32m$
• C. $100m$
• D. $64m$

Answer 1

The correct option is C $100m$

Given, $s=48t-16t^2$

On differentiating w.r.t. $t$, we get

$\frac{ds}{dt}=48-32t$

For greatest height, $v=\frac{ds}{dt}=0$

$\Rightarrow 48-32t=0$

$\Rightarrow t=\frac{3}{2}$

$\therefore s=48\times \frac{3}{2}-16{\left(\frac{3}{2}\right)}^2=36m$

$\therefore$ The total height $=64+36=100m$.