Question

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

Answer 1

Suppose, PR = 2x

So, PQ = QR = x

The ball starts with zero velocity. Suppose it takes time t1 to cover PQ and time t2 to cover QR.

Now,

Using,

S = UT + ½ AT2

=> 2x = 0 + ½ g(t1 + t2)^2

=> x = ¼ g(t1 + t2)^2

=> 4x = g(t1 + t2)^2 ……………..(1)

Again,

x = 0 + ½ g(t1)^2

=> 2x = g(t1)^2 …………………(2)

Now,

(1)/(2) => 2 = (t1 + t2)^2/(t1)^2

=> [(t1 + t2)/t1]^2 = 2

=> [1 + t2/t1] = √2

=> t2/t1 = √2 – 1

=> t1 : t2 : 1 : (√2 – 1)