Aball is thrown upward with an initial vertical velocity of v0 to a maximum height of hmax and falls back toward earth. on the way down, it is caught at the same height at which it was thrown upward. b b b b b b b b b bbb b b b b b b b b v0 hmax if the total time the ball remains in the air is t, find its speed when caught. the acceleration of gravity is g. neglect air resistance.

The ball was thrown at the speed of .

Maximum height achieved is

Time of flight is t.

Now, the time the ball takes to achieve maximum height = the time taken by ball to fall back =

let us just consider the second half of the flight. At , the velocity would be zero. let us consider as the initial velocity for the second half of the flight i.e.

Using the equation of motion:

where,   is the final velocity, a is the acceleration, t is the time taken.

Because the ball would fall under gravity, hence a=g and time of flight would be t/2