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An acrobat is on a platform that is 81 feet in the air. She jumps with an initial upward vertical velocity of 4 ft/s. Write a quadratic function to represent the height h in feet of the acrobat t seconds after the jump. If a safety net is placed 9 feet above the ground, how long will it take for her to land safely on the net?
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GPT-5 mini
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Use g = 32 ft/s² downward. The height function is
h(t) = -16t² + 4t + 81 (feet).
Set h(t) = 9 and solve:
-16t² + 4t + 81 = 9 → -16t² + 4t + 72 = 0 → 4t² - t - 18 = 0.
t = [1 ± √(1 + 288)]/8 = [1 ± 17]/8, so t = 18/8 = 9/4 = 2.25 s (discard negative root).
She lands safely on the net 2.25 seconds after the jump.
h(t) = -16t² + 4t + 81 (feet).
Set h(t) = 9 and solve:
-16t² + 4t + 81 = 9 → -16t² + 4t + 72 = 0 → 4t² - t - 18 = 0.
t = [1 ± √(1 + 288)]/8 = [1 ± 17]/8, so t = 18/8 = 9/4 = 2.25 s (discard negative root).
She lands safely on the net 2.25 seconds after the jump.
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