The time required for a dropped object to hit the ground is given by $t \equiv \sqrt { \frac { 2 h } { g } }$ , where h is the vertical distance traveled and g is the acceleration due to gravity, assumed to be 32.2 feet per second squared. How tall a building is required for an object to take 9 seconds to fall to the ground?
A) h = 2,409.1 feet
B) h = 1,142.8 feet
C) h = 1,304.1 feet
D) h = 2,035.1 feet
E) h = 3,865.4 feet

Question

Quizplus · Accepted Answer

We know that the time taken for the object to fall is given as 9 seconds, and acceleration due to gravity is 32.2 feet per second squared.
Using the formula, 
t = sqrt(2h/g)
9 = sqrt(2h/32.2)
Squaring both sides, 
81 = 2h/32.2
Multiplying both sides by 32.2, 
2h = 2604.2 
h = 1302.1 feet
Therefore, the height of the building required for an object to take 9 seconds to fall to the ground is approximately 1304.1 feet. Hence, the answer is option C.

The Time Required for a Dropped Object to Hit the Ground