A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is traveling at 30.3 m/s when it strikes a person's head (1.5 m above the ground), how tall is the building? Neglect air resistance.
A) 48 m
B) 47 m
C) 50 m
D) 51 m

48m

Explanation:

First we need to calculate the distance from the person head to the top of the building using the equation of motion

v² = u²+2gH where

v is the final velocity of the balloon= 30.3m/s

u is the initial velocity of the balloon = 0m/s

g is the acceleration due to gravity = 9.81m/s²

H is the distance between the person head and the top of the building

Substituting into the formula, we have;

30.3² = 0²+2(9.81)H

918.09 = 19.62H

H = 918.09/19.62

H = 46.79m

To know how tall the building is, we will add the height of the building above the ground and the distance between the man's head and the top of the building. This will give;

Ht = 46.79+1.5

Ht = 48.29m

Ht is approximately 48m

Therefore the building is 48m tall

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