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

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.