Question

A balloon is at rest in the air at a height of 1960 m. A ball is dropped from the balloon. Determine
(i) The time taken by the ball to reach the ground.
(ii) The velocity with which it reaches the ground.

Answer 1

Given:

A balloon is at rest in the air at a height of 1960 m. A ball is dropped from the balloon.

To find:

• Time taken by ball to reach ground.
• Velocity of striking ground.

Calculation:

• Since the balloon is stationary, the initial velocity of ball will be zero.

• Also, the gravitational acceleration is 9.8 m/s².

Applying EQUATIONS OF KINEMATICS:

$h = ut + \dfrac{1}{2} a {t}^{2}$

$\implies \: 1960 = 0(t) + \dfrac{1}{2} \times (9.6) \times {t}^{2}$

$\implies \: 1960 = 4.9 \times {t}^{2}$

$\implies \: {t}^{2} = 400$

$\implies \: t= \sqrt{400}$

$\implies \: t= 20 \: sec$

So, the ball takes 20 seconds to reach ground.

• Now, let striking velocity be v.

$\therefore \: v = u + at$

$\implies \: v = 0 + (9.6) \times 20$

$\implies \: v = 198 \: m {s }^{ - 1}$

So, final velocity with which ball strikes ground is 198 m/s .