Question

A tennis ball is thrown up and reaches a height of 4.05 m before coming down. What was its initial velocity? How much total time will it take to come down? Assume g = 10 m/s²?

Answer 1

Given: Distance travelled by the ball (s) = 4.05 m,

acceleration a = g = 10 m/s²

To find:

1. Initial velocity (u)

2. Time taken (t)

Formulae:

1. v² = u² + 2 as

2. s = ut + `1/2` at²

Calculation: For upward motion of the ball, (v) = 0.

a = –g = –10 m/s²

From formula (i),

0 = u² + 2(- 10) × 4.05

∴ u² = 81

∴ u = 9 m/s

For downward motion of the ball, (u) = 0.

a = g = 10 m/s² 

From formula (ii),

`4.05 = 0 + 1/2 xx 10 "t"^2`

∴ `"t"^2 = 4.05/5` = 0.81

∴ t = 0.9 s

Time for upward journey of the ball will be the same as time for downward journey i.e., 0.9 s.

∴ Total time taken = 2 × 0.9 = 1.8 s

1. The initial velocity of the ball is 9 m/s.

2. The total time taken by the ball to reach the ground is 1.8 s.