Answer:
t = 7.875 seconds
Explanation:
Comment
The formula itself gives you the answer almost directly.
Givens
S(t) = 217 feet
a = - 16
b = 12
Formula
S(t) = - 16t^2 + 126t
0 = -16t^2 + 126t - 217
Solution
You must use the formula for solving a quadratic.
t = (-b +/- (√b^2 - 4*ac)/2a Substitute the gives into the quadratic formula
t = (-126 +/- √126^2 - 4(-16)(-217) )
t = (-126 +/- √15876) 2*-16
t = (-126 +/- 126) / 2* - 16
There are 2 values for t. One is not usable.
t = (-126 + 126)/-32 = 0
so t = 0 so that's impossible
t = - 252 / - 32 Combined -126 and - 126
t = 7.875 seconds.
After 7.875 seconds, the ball has gone up 217 feet. The reason you are getting only one answer is likely that you are getting the going up distance. But after the ball has reached its highest point if may have the going down distance = 217 feet from the ground. The formula does not provide it however.