During a "big air" competition, snowboarders launch themselves from a half pipe, perform tricks in the air, and land back in the half pipe. Shaun White’s initial velocity is 24 feet/sec and the initial height is 16.4 feet.
a) Use the vertical motion model to write an equation that models the height h (in feet) of a snowboarder as a function of the time t (in seconds) he is in the air.
b) How long is Shaun White in the air if she lands 13.2 feet above the base of the half pipe? Round your answers to the nearest tenth of a second.
a) The function is :
h = -16t^2 + 24t + 16.4
13.2 = -16t^2 + 24t + 16.4 subtract 13.2 from each side
0 = -16t + 24t + 3.2 multipl through by - 1
16t^2 - 24t - 3.2 = 0 divide through by 3.2
5t^2 - 7.5t - 1 = 0
Solving this for t we get ≈ 1.6 seconds