4

Set 11: Quadratic Equations (Intermediate)

Explanation

Answer: A

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

✓ Correct
B.

3.00 seconds

C.

1.50 seconds

D.

0.12 seconds

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Set h(t)=0h(t) = 0 and use the quadratic formula. 1. −16t2+48t+6=0-16 t^2 + 48 t + 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.

Key Steps:

•

The correct answer is 3.12 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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