Question

A ball dropped from a point $P$ crosses a point $Q$ in $t$ second. if $R$ and S are points such that, $PQ=QR=RS$, the time taken by the ball to travel from $R$ to $S$ is:

• A. $(\sqrt{2}-1)t$
• B. $(\sqrt{3}-\sqrt{2})t$
• C. $\sqrt{3}t$
• D. $(\sqrt{3}-1)t$

Answer 1

Answer: (B)

$(\sqrt{3}-\sqrt{2})t$

From, $R$to$S$ time taken is $t^{\prime }$
$3x=\frac{1}{2}g{t}_2^2-\left(1\right)$
$2x=\frac{1}{2}g{t}_1^2-\left(2\right)$
$x=\frac{1}{2}g{t}^2-\left(3\right)$
$e{q}^n\frac{\left(2\right)}{\left(3\right)}\Rightarrow t_1=\sqrt{2t}$
$\frac{e{q}^n\left(1\right)}{e{q}^n\left(2\right)}\Rightarrow \frac{3}{2}=\frac{t_2^2}{t_1^2}$
$\Rightarrow t_2=\sqrt{3}$t
$\Rightarrow$ So, time from R to S $\Rightarrow t^{\prime }=t_2-t_1=(\sqrt{3}-\sqrt{2})t$