Question

A potato is launched vertically upward with an initial velocity of 34ft/s from a potato gun at the top of a building that is 15 feet tall. The height of the potato in feet after t seconds is given by s(t)=−16t2+34t+15. Determine how long the potato is in the air. Enter an exact answer.

Answer 1

It will be in the air as long as s(t) > 0
So let's see when it hits the ground
-16t^2 + 34t + 15 = 0
16t^2 - 34t - 15 = 0
t = (34 ± √2116)/32
= (34 ± 46)/32 = 2.5 or a negative which must be rejected

so the potato is in the air for 2.5 seconds