Question

An acrobat is on a platform that is 81 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

Use h(t) = h0 + v0 t - (1/2) g t^2 with g = 32 ft/s^2:

h(t) = 81 + 44t - 16t^2.

Set h(t) = 99 and solve:
81 + 44t - 16t^2 = 99
⇒ 16t^2 - 44t + 18 = 0 ⇒ 8t^2 - 22t + 9 = 0.

t = [22 ± sqrt(22^2 - 4·8·9)]/16 = [22 ± 14]/16 ⇒ t = 0.5 s or t = 2.25 s.

She passes the net at 0.5 s on the way up and lands on it at 2.25 seconds after the jump.