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Snezhnost [94]
3 years ago
5

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?
Physics
1 answer:
Margaret [11]3 years ago
7 0

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

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