Question

An iron ball of mass 3 kg is released from a height of 125 m and falls freely to the ground. Assuming that the value of g is 10 m/s², calculate:

1. Time taken by the ball to reach the ground.
2. Velocity of the ball on reaching the ground.

An iron ball of mass 3 kg is released from a height of 125 m and falls freely to the ground. Assuming that the value of g is 10 m/s², calculate time taken by the ball to reach the ground.

Answer 1

Given:

Mass of the iron ball, m = 3 kg

Initial velocity, u = 0 m/s

Distance travelled by the ball, s = 125 m

Acceleration, a = g = 10 m/s²

(a) Newton’s second equation of motion gives,

${\displaystyle s=ut+\frac{1}{2}a{t}^2}$

${\displaystyle 125=0t+\frac{1}{2}\times 10\times t^2}$

125 = 5t²

${\displaystyle t^2=\frac{125}{5}}$

t² = 25

t = ${\displaystyle \sqrt{25}}$

t = 5 s

The ball takes 5 seconds to reach the ground.

(b) According to Newton’s first equation of motion,

Final velocity = v = u + a t

= 0 + (10 × 5)

= 50 m/s

The velocity of the ball on reaching the ground is 50 m/s.