10
advanced-math

An object dropped from a height falls according to d=16t2d = 16t^2, where dd is distance in feet and tt is time in seconds. How long does it take to fall 64 feet?

A

2 seconds

B

4 seconds

C

8 seconds

D

16 seconds

Correct Answer: A

Choice A is the correct answer. We are given d=64d = 64 and need to find tt.

  1. Substitute d=64d=64: 64=16t264 = 16t^2.
  2. Divide by 16: 4=t24 = t^2.
  3. Take the square root: t=±2t = \pm 2.

Since time cannot be negative, t=2t = 2 seconds.

Choice B is incorrect because 16(4)2=25616(4)^2 = 256. Choice C is incorrect because 16(8)2=102416(8)^2 = 1024. Choice D is incorrect because it solved linearly 16t=6416t = 64.