The time t , in seconds, for a free falling object to fall d feet is given by $t = \sqrt { \frac { d } { 16 } }$ . If a construction worker drops a nail from a building and observes it strike a water puddle after 5 seconds, what is the height from which the nail was dropped?
A) 80 feet
B) 25 feet
C) $100$ feet
D) $400$ feet
E) 5 feet

Question

Quizplus · Accepted Answer

From the given formula $t=\sqrt{\frac{d}{16}}$, we know that $t$ is directly proportional to the square root of the height $d$. So, if the time taken by the falling object to reach the ground is 5 seconds, then we can say that $\sqrt{d}=\sqrt{16t}$, which simplifies to $\sqrt{d}=4\sqrt{t}$. Substituting the value of $t=5$ seconds, we get $\sqrt{d}=20$, which gives us the value of $d$ as 400. Hence, the height from which the nail was dropped is 400 feet. Therefore, the answer is D.

The Time T , in Seconds, for a Free Falling t=d16t = \sqrt { \frac { d } { 16 } }t=16d​​

The Time T , in Seconds, for a Free Falling $t = \sqrt { \frac { d } { 16 } }$