When is the potato at the height of 34ft?

Question

A potato is launched vertically upward with an initial velocity of 71ft/s from a potato gun at the top of a building that is 79 feet tall. The height of the potato in feet after t seconds is given by s(t)=−16t2+71t+79. When is the potato at a height of 34ft? Enter an exact answer.

Answer 1

s(t) = − 16t² + 71t + 79.= 34; 16t² - 71t - 45 = 0; t = (71 - √71² + 180·16)/32 = 5 s

Answer 2

s(t) is the height in feet and includes the initial starting height of 79 ft and the initial velocity of 71 ft/s - so that information is unnecessary for the problem.

This is not a calculus problem at this point. You want to solve for the t given an s of 34 ft:

34 = -16t² +71t + 79 or 16t² - 71t - 45 = 0

Use the quadratic formula and keep the solution that is > 0.

Answer 3

−16t²+71t+79 = 34

−16t²+71t+45=0

By quadratic equation,

t = -9/16, 5

Choose 5 seconds