Problem 6 on Motion in a Straight Line

Description:

Problem

A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take in reaching the ground.

Solution

Analyzing motion path of the ball,

When the ball is released from the balloon, it possesses an upward velocity of 7 m/s. Therefore, the ball will move upwards, attain a maximum height and then eventually descend down.

Assuming sign convention to be −

• Upwards – Positive
• Downwards – Negative

We can say that,

Initial Velocity, u = 7 m/s

Acceleration, g = −9.8 m/s²

Displacement, S = -60 m

Using, S = ut + 1/2 at², we get,

-60 = 7t + 1/2 (-9.8) t²

4.9 t² - 7t - 60 = 0

t = 4.28 s ≈ 4.3 s