10

Set 17: Quadratic Equations (Intermediate)

Explanation

Answer: A

A diver jumps from a 10m platform. Height is h(t)=−4.9t2+4t+10h(t) = -4.9t^2 + 4t + 10. When does the diver reach the water (h=0h=0)?

A.

1.90 seconds

✓ Correct
B.

2.50 seconds

C.

0.41 seconds

D.

1.00 seconds

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve −4.9t2+4t+10=0-4.9 t^2 + 4 t + 10 = 0 using the quadratic formula. 1. t=−4±16−4(−4.9)(10)−9.8t = \frac{-4 \pm \sqrt{16 - 4(-4.9)(10)}}{-9.8}. 2. t=−4±16+196−9.8=−4±212−9.8t = \frac{-4 \pm \sqrt{16 + 196}}{-9.8} = \frac{-4 \pm \sqrt{212}}{-9.8}. 3. t≈−4±14.56−9.8t \approx \frac{-4 \pm 14.56}{-9.8}. 4. Positive solution: t≈1.89t \approx 1.89 seconds (rounds to 1.90). Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is 1.90 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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