Question

The equation $y = -16t^2 + 26t + 105$ describes the height (in feet) of a ball tossed up in the air at 26 feet per second from a height of 105 feet above the ground. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest tenth.

Answer 1

Set y = 0 and solve:
-16t^2 + 26t + 105 = 0
16t^2 - 26t - 105 = 0

t = [26 ± sqrt(26^2 + 4·16·105)] / (2·16)
= [26 ± sqrt(676 + 6720)] / 32
= [26 ± 86] / 32

Positive root: t = (26 + 86)/32 = 112/32 = 3.5.

Rounded to the nearest tenth: 3.5 seconds.