Question

An acrobat is on a platform that is 8181 feet in the air. She jumps with an initial upward vertical velocity of 44 ​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 99 feet above the​ ground, how long will it take for her to land safely on the​ net?

Answer 1

Take gravity as -32 ft/s^2, so the height function is
h(t) = -16t^2 + 44t + 8181 (feet, t in seconds).

Set h(t) = 99 and solve:
-16t^2 + 44t + 8181 = 99
=> -16t^2 + 44t + 8082 = 0
=> 16t^2 - 44t - 8082 = 0.

t = [44 ± sqrt(44^2 + 4·16·8082)] / (2·16)
≈ [44 ± 360.272] / 32.

The positive root is t ≈ (44 + 360.272)/32 ≈ 23.89 seconds.

So she will land safely on the net after about 23.9 seconds.