Question

A particle is dropped under gravity from rest from a height $h$ and it travels a distance $16h/25$ in the last second, the height $h$ is (take $g=10m/s^2$)

• A. $31.25m$
• B. $122.5m$
• C. none of these
• D. $62.50m$

Answer 1

The correct option is A $31.25m$

Given, particle dropped from the height $h$, so its initial velocity $u=0$,
Let the total time in which body is in motion be $t$.
So, $h=ut+\frac{1}{2}a{t}^2$
$h=\frac{1}{2}g{t}^2\dots \left(i\right)$
The distance travelled in last second.
$s_n=u+\frac{a}{2}(2n-1)$
$\frac{16h}{25}=0+\frac{g}{2}(2t-1)\dots \left(ii\right)$
By solving equation $\left(i\right)$ and $\left(ii\right)$,
we get, $t=\frac{5}{2}s$ and $h=31.25m$