Answer
$t=4.5175$ $s$
Work Step by Step
According to question:
$\frac{d^{2}y}{dt^{2}}=g$, $y(0)=0$, $\frac{dy}{dt}(0)=0$
On integration,
$\frac{dy}{dt}=gt+c_1$
Using inital condition put $t=0$ and $\frac{dy}{dt}(0)=0$
$0=g\cdot0+c_1$
$c_1=0$
$\frac{dy}{dt}=gt$
On integrating again,
$y=\frac{1}{2}gt^2+c_2$
Using intial condition $y(0)=0$,
$0=\frac{1}{2}g\cdot(0)^2+c_2$
$c_2=0$
So equation becomes $y=\frac{1}{2}gt^2$
Put $y=100$ $m$ and $g=9.8$ ${m}{s^{-2}}$
$100=\frac{1}{2}(9.8)(t^2)$
$t=\sqrt{20.4081}$ $s$$=4.5175$ $s$
