Question

A helicopter hovers over a mountain top, and a professional snowboarder drops onto the snow 252525 feet below. the snowboarder's height off the ground, in feet, while falling can be modeled by a quadratic function of seconds of falling, ttt, which has the form h(t) = d - at^2h(t)=d−at 2 h, left parenthesis, t, right parenthesis, equals, d, minus, a, t, start superscript, 2, end superscript. if the snowboarder is still 212121 feet above the ground after falling for 0.50.50, point, 5 seconds, how long does the entire 252525 foot drop take? round your answer to the nearest hundredth of a second.

Answer 1

Given:
h(t) = 25 - a·t²
h(0.5) = 21

Find:
t such that h(t) = 0

Solution:
h(0.5) = 25 - a·0.5² = 21
25 - 21 = a/4
4·4 = a = 16
Then
h(t) = 25 - 16t²
We want h(t) = 0, so
0 = 25 - 16t²
16t² = 25
t² = 25/16 = (5/4)²
t = 5/4 = 1.25

It takes 1.25 seconds for the entire 25 ft drop.