A student drops a water balloon from tall building trying to hit her roommate on the ground below (and misses). After dropping the balloon, the student ducks behind cover and hears a splash 4 seconds later. Given that the speed of sound in air is 331 m/s, find the height of the building. (neglect air resistance).

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aristocles aristocles · Answer 1 · 2019-09-09T03:30:53+02:00

Answer:

H = 70.4 m

Explanation:

Here first of all the balloon will drop to the the floor under free fall motion and then the sound of splash will come up at constant speed

so we will say that if the total height is H

so the time to fall is given as

[tex]H = \frac{1}{2}gt^2[/tex]

now we have

[tex]t_1 = \sqrt{\frac{2H}{g}}[/tex]

also we know that the time to come the sound upwards is

[tex]t_2 = \frac{H}{v}[/tex]

so we will have

[tex]t_1 + t_2 = T[/tex]

[tex]\sqrt{\frac{2H}{g}} + \frac{H}{v} = T[/tex]

now plug in all data

[tex]\sqrt{\frac{2H}{9.81}} + \frac{H}{331} = 4[/tex]

by solving above equation we have

H = 70.4 m