Question

A ball dropped from a point $P$ crosses a point $Q$ in $t$ seconds. The time taken by it to travel from $Q$ to $R$, if $PQ=QR$, is:

• A. $t$
• B. $\sqrt{2}t$
• C. $2t$
• D. $(\sqrt{2}-1)t$

Answer 1

The correct option is D $(\sqrt{2}-1)t$

Assuming $PQ=QR$, we get:

$x=\frac{1}{2}g{t}^2-\left(1\right)$
and, $2x=\frac{1}{2}g{t}_1^2-\left(2\right)$
Dividing $\left(1\right)$ and $\left(2\right),\frac{1}{2}=\frac{t^2}{t_1^2}\Rightarrow t_1=\sqrt{2}t$
Now, time from Q to R $\Rightarrow t_1-t=\sqrt{2}t-t$$=t(\sqrt{2}-1)$