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For the vertical motion model h left parenthesis t right parenthesish(t)equals=negative 16 t squared plus 77 t plus 9−16t2+77t+9, identify the maximum height reached by an object and the amount of time the object is in the air to reach the maximum height.
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GPT-5 mini
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The height function is h(t) = −16t^2 + 77t + 9 (t in seconds, h in feet).
- Time to reach the maximum: t = −b/(2a) = 77/(2·16) = 77/32 ≈ 2.40625 s.
- Maximum height: h(77/32) = 6505/64 ≈ 101.640625 ft.
(If you meant total time in the air until it hits the ground, solve h(t)=0: the positive root is t ≈ 4.93 s.)
- Time to reach the maximum: t = −b/(2a) = 77/(2·16) = 77/32 ≈ 2.40625 s.
- Maximum height: h(77/32) = 6505/64 ≈ 101.640625 ft.
(If you meant total time in the air until it hits the ground, solve h(t)=0: the positive root is t ≈ 4.93 s.)
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