3
advanced-math

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

B

2.50 seconds

C

0.41 seconds

D

1.00 seconds

Correct Answer: A

Choice A is the correct answer. Solve −4.9t2+4t+10=0-4.9t^2 + 4t + 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.

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Set 17: Quadratic Equations and Functions 17