A ball is dropped from a balloon ascending at a speed of 7 m/s . If the balloon was at a height of 60 m at the time the ball was dropped, determine the time taken by the ball to reach the ground in seconds.

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Quantrex Academy · Accepted Answer

Correct answer: B. (30)/(7) s

Taking the upward direction as positive.

Initial velocity of the ball,

u = 7 \text{ m/s}

Displacement of the ball,

s = -60 \text{ m}

Acceleration due to gravity,

a = -9.8 \text{ m/s}^2

Using the equation of motion

s = ut + \dfrac{1}{2}at^2

:

-60 = 7t - \dfrac{1}{2}(9.8)t^2

-60 = 7t - 4.9t^2

4.9t^2 - 7t - 60 = 0

Multiplying by

10

on both sides:

49t^2 - 70t - 600 = 0

49t^2 - 210t + 140t - 600 = 0

7t(7t - 30) + 20(7t - 30) = 0

(7t + 20)(7t - 30) = 0

Since time cannot be negative, we get

7t - 30 = 0 \Rightarrow t = \dfrac{30}{7} \text{ s}

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A ball is dropped from a balloon ascending at a speed of 7 m/s . If...

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