4
advanced-math

A rocket is launched. Its height is h(t)=−16t2+128th(t) = -16t^2 + 128t. How long is the rocket in the air?

A

8 seconds

B

4 seconds

C

16 seconds

D

128 seconds

Correct Answer: A

Choice A is the correct answer. Find when it hits the ground (h=0h=0).

  1. −16t2+128t=0-16t^2 + 128t = 0.
  2. Factor: −16t(t−8)=0-16t(t - 8) = 0.
  3. Roots: t=0t=0 (launch) and t=8t=8 (landing).
  4. Total time in air is 8 seconds.

Choice B is incorrect because it is the time to max height. Choice C is incorrect. Choice D is incorrect.

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Set 17: Quadratic Equations and Functions 17