Question

The function h=−16t2+48t+6
models the height of a shot put, in feet, t
seconds after it is thrown. Find the time when the shot put is at a height of 30 feet while it is on its way down.

Graph of a parabolic trajectory showing height over time.
(1 point)
Responses

0.6 seconds
0.6 seconds

3.1 seconds
3.1 seconds

2.4 seconds
2.4 seconds

1.5 seconds

Answer 1

Solve -16t^2 + 48t + 6 = 30:
-16t^2 + 48t - 24 = 0 → divide by -8 → 2t^2 - 6t + 3 = 0.
t = [6 ± sqrt(36 - 24)]/4 = (3 ± √3)/2 ≈ 0.63 s and 2.37 s.

The shot is on the way down after the peak (t = 1.5 s), so the correct time is about 2.4 seconds.