10

Set 12: Quadratic Equations

Explanation

Answer: A

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

✓ Correct
B.

4 seconds

C.

8 seconds

D.

16 seconds

Detailed Explanation

Choice A is correct. Choice A is the correct answer. We are given d=64d = 64 and need to find tt. 1. Substitute d=64d=64: 64=16t264= 16 t^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.

Key Steps:

The correct answer is 2 seconds

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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