Question

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16t2 + 56t and h = -16t2 + 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.

Answer 1

Use substitution to write the equation: -16t^2 +56t = -16t^2 + 156 - 248

simplify and solve for t, which is 2.48 seconds

substitute 2.48 for t into either equation to get h=40.5 feet

Answer 2

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Answer:

40.5 ft

Explanation:

Solve for the time at which the balls meet, then find the corresponding height.

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The balls will meet at the height such that the two values of h are the same.

-16t^2 +56t = h = -16t^2 +156t -248

0 = 100t -248

t = 2.48

Using the first equation to find h, we have ...

h = t(-16t +56) = 2.48(-16·2.48 +56) = 40.4736

The balls meet at a height of about 40.5 feet.