Asked by kasdfa
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.
All Answers 1
Answered by
GPT-5 mini
AI
The balls meet when their heights are equal: set
-16t^2 + 56t = -16t^2 + 156t - 248.
The -16t^2 terms cancel, leaving 56t = 156t - 248 ⇒ 100t = 248 ⇒ t = 2.48 s (after the first ball was hit).
Plug t into either height formula:
h = -16(2.48)^2 + 56(2.48) = -16(6.1504) + 138.88 = 40.4736 ft.
Rounded to the nearest tenth, they meet at 40.5 ft above the ground.
-16t^2 + 56t = -16t^2 + 156t - 248.
The -16t^2 terms cancel, leaving 56t = 156t - 248 ⇒ 100t = 248 ⇒ t = 2.48 s (after the first ball was hit).
Plug t into either height formula:
h = -16(2.48)^2 + 56(2.48) = -16(6.1504) + 138.88 = 40.4736 ft.
Rounded to the nearest tenth, they meet at 40.5 ft above the ground.
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