Question

A student throws a ball vertically. 2.0 seconds later, it is caught by a friend on a balcony 5.0 m above the point of release. When did the ball first pass the friend on the balcony and how fast was it going at that instant?

Answer 1

Let u be the initial velocity of the ball. The ball undergo uniformly accelerated motion at acceleration g=-9.8m/s². The motion of the ball is governed by the Kinematics equations for uniformly accelerated motion. To find the initial velocity we use

Ball is at height h=5.0m at time t=2.0s

The ball reaches the friend twice: first time when the ball is on its way up, second time when it is on its way down. We want to find the time when the ball first reaches the friend,

This is quadratic equation in time, the roots of quadratic equation are

The time is

The ball first reaches the friend at time 0.51s and then again at 2.0s.

The velocity at this instant is