Question

A juggler throws balls is to air and catch them. He throws one all whenever the previous ball is at its highest point. How high do the balls rise, if he throws n balls every second? (Acceleration due to gravity is g).

(1) g/n²

(2) g/2n²

(3) 2g/n²

(4) 2g

Answer 1

(2) g/2n²

Number of balls thrown is 1 s = n, Time interval between two balls = 1/n

Now, he throws one when the previous one thrown reaches the maximum height.

∴ Time taken by one ball to reach the maximum height is

t = 1/n ....(1)

Let u be the velocity with which the ball is thrown. Then the velocity at the highest point is zero, and so,

0 = u – gt

or u = g/n .....(2)