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.
Answers
Given : 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.
To find : the height at which the balls meet.
Solution:
t is the time that has passed since the first ball was hit.
so at given time height should be same for balls to meet
Hence
Equating h = -16t² + 56t & h = -16t² + 156t - 248
=> -16t² + 56t = -16t² + 156t - 248
=> 100t = 248
=> t = 2.48
After 2.48 secs of first ball hit balls will meet
height = - 16(2.48)² + 56(2.48) or -16(2.48)² + 156(2.48) - 248
Height = 40.4736 ≈ 40.5
Height at which balls meet = 40.5
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