Q. Points $ P $ , $ Q $ and $ R $ are in a vertical line such that $ PQ = QR $ . A ball at $ P $ is allowed to fall freely. The ratio of times of descent through $ PQ $ and $ QR $ is
Motion in a Straight Line
Solution:
$ PQ = QR = h $
$ h=\frac{1}{2}gt^{2}_{1} $ and $ 2h=\frac{1}{2}g\left(t_{1}+t_{2}\right)^{2}\quad\left(\because u=0\right) $
$ \frac{1}{2} =\frac{t^{2}_{1}}{\left(t_{1}+t_2\right)^{2}} $ or $ \frac{1}{\sqrt{2}}=\frac{t_{1}}{\left(t_{1}+t_{2}\right)} $
$ t_{1}+t_{2}=\sqrt{2}t_{1} $ or $ t_{1}\left(\sqrt{2}-1\right)=t_{2} $
$ \therefore \frac{t_{1}}{t_{2}}=\frac{1}{\left(\sqrt{2}-1\right)} $ .
