Points ` P, Q` and `R` are in vertical line such that ` PQ =QR`. A ball at (P) is allowed to fall freely. What is the ratio of the times of descent through PQ and QR ?

Explanation

Let ` t_(1), t_(2) `be the times of descent through ` PQ` and `QR` respectively. Let ` PQ=QR=y`. Then
` y =1/2 gt_(1)^(2) and 2 y =1/2 g (t_(1) +t_(2))^(2)`
or ` (2 y)/y =((t_(1) + t_(2))^(2)/t_(1)^(2)` or ` sqrt 2 =(t_(1) +t_(2))/t_(1) 1 + t_(2)/t_(1)`
or ` t_(2)/t_(1) =sqrt 2-1 or t_(1)/t_(2) =1/(sqrt2 -1) =1 : (sqrt -1)`.