Question

A stone projected vertically upwards raises 's' feets in 't' second were s =$112t-16t^2$. Then maximum height it reached is

Answer 1

$s=112t-16t^2$

Differentiating above equation w.r.t. $t$, we have

$\frac{ds}{dt}=112-32t.....\left(1\right)$

Now,

$\frac{ds}{dt}=0$

$112-32t=0$

$\Rightarrow t=\frac{112}{32}=3.5$

Now, differentiating ${eq}^n\left(2\right)$ w.r.t. $t$ we have

$\frac{d^{2}s}{d{t}^2}=-32<0$

$\because \frac{d^{2}s}{d{t}^2}<0$

Therefore,

Substituting the value of $t$ in ${eq}^n\left(2\right)$, we have

$s=112\times 3.5-16{\left(3.5\right)}^2=196$

Hence the maximum height the stone reached is $196m$.