Question

Suppose the balloon is descending with a constant speed of 4.2 m/s when the bag of sand comes loose at a height of 35 m. What is the amount of time the bag is in the air?

Answer 1

Answer:

2.28 s

Explanation:

Let g = 9.8 m/s2 and neglect air resistance. The box of sand with an initial velocity of 4.2m/s in free fall would yield the following equation of motion

$s = v_0t + gt^2/2$

$35 = 4.2t + 9.8t^2/2$

$4.9t^2 + 4.2t - 35 = 0$

$t= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$t= \frac{-4.2\pm \sqrt{(4.2)^2 - 4*(4.9)*(-35)}}{2*(4.9)}$

$t= \frac{-4.2\pm26.53}{9.8}$

t = 2.28 or t = -3.14

Since t can only be positive we will pick t = 2.28 s