2
advanced-math

Using the same model h(t)=−16t2+48t+6h(t) = -16t^2 + 48t + 6, when does the ball hit the ground?

A

3.12 seconds

B

3.00 seconds

C

1.50 seconds

D

0.12 seconds

Correct Answer: A

Choice A is the correct answer. Set h(t)=0h(t) = 0 and use the quadratic formula.

  1. −16t2+48t+6=0-16t^2 + 48t + 6 = 0.
  2. t=−48±482−4(−16)(6)2(−16)t = \frac{-48 \pm \sqrt{48^2 - 4(-16)(6)}}{2(-16)}.
  3. t=−48±2304+384−32=−48±2688−32t = \frac{-48 \pm \sqrt{2304 + 384}}{-32} = \frac{-48 \pm \sqrt{2688}}{-32}.
  4. t≈−48±51.85−32t \approx \frac{-48 \pm 51.85}{-32}.
  5. t≈−0.12t \approx -0.12 (discard) or t≈3.12t \approx 3.12 seconds.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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Set 17: Quadratic Equations and Functions 17