Question

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?

 

Answer 1

Given:
Height of the balloon from the ground, s = 60 m
Balloon is moving upwards with velocity 7 m/s.
The balloon and the ball are moving upwards with the same speed.
When the ball is dropped, its initial velocity (u) is −7 m/s.
Acceleration due to gravity, a = g = 9.8 m/s²
Using the equation of motion, we have:

\[s = \text{ ut }  + \frac{1}{2}a t^2\]

\[60 = - 7t + \frac{1}{2} \times 9 . 8 \times t^2 \]
\[ \Rightarrow 60 = - 7t + 4 . 9 \times t^2 \]
\[ \Rightarrow 4 . 9 t^2 - 7t - 60 = 0\]
\[t = \frac{7 \pm \sqrt{49 - 4 \times 4 . 9 \times \left( - 60 \right)}}{2 \times 4 . 9}\]
\[t = \frac{7 \pm \sqrt{\left( 49 + 1176 \right)}}{9 . 8}\]
\[t = \frac{7 \pm 35}{9 . 8}\]

We will ignore the −ve sign in the above equation because time can never be negative.

\[\therefore t = \frac{7 + 35}{9 . 8} = 4 . 28 s\]

Time taken by the ball to reach the ground = 4.3 s