Question

If a body travels half its total path in the last second of its fall from rest, find the time of its fall. Take $g=10{\text{m/s}}^2$.

• A. $3.4\text{s}$
• B. $4.4\text{s}$
• C. $4.8\text{s}$
• D. $5.4\text{s}$

Answer 1

The correct option is A $3.4\text{s}$

If $H$ be the total height body falls from rest, total time to fall is $t=\sqrt{\frac{2H}{g}}$
It is given that the body falls $\frac{H}{2}$ distance in time $(t-1)$, thus we have $t-1=\frac{\sqrt{2\left(H/2\right)}}{g}$

From above equations,
$\sqrt{\frac{2H}{g}}-\sqrt{\frac{H}{g}}=1$
$\sqrt{\frac{H}{g}}(\sqrt{2}-1)=1$
$\sqrt{\frac{H}{g}}=(\sqrt{2}+1)$
Total time of fall is $t=\sqrt{\frac{2H}{g}}=(\sqrt{2}+2)=3.4\text{s}$