During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = - 16t^2 + 56t and h = - 16t^2 + 156t - 248, where t is the time that has passed since the first ball was hit. Explain how to find the height at which the balls meet. Then find the height to the nearest tenth.

Question

Mathematics

Harvey

17 February, 01:22

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = - 16t^2 + 56t and h = - 16t^2 + 156t - 248, where t is the time that has passed since the first ball was hit. Explain how to find the height at which the balls meet. Then find the height to the nearest tenth.

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Answers (1)

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Madden Hancock · Answer 1

2.5 seconds since the first ball was hit.

Step-by-step explanation:

The equations that model the heights are:

h = - 16t² + 56t h = - 16t² + 156t - 248

When the balls meet, both heights are equal, therefore:

-16t² + 56t = - 16t² + 156t - 248

-16t² + 56t + 16t² - 156t + 248 = 0

- 100t + 248 = 0

248 = 100t

248/100 = t

t = 2.48 ≈ 2.5