SOLUTION: A goalie kicks a soccer ball with an upward velocity of 65 feet per second, and her foot meets the ball 1 foot off the ground. The quadratic function h=16tsquared + 65t + 1 represe

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A goalie kicks a soccer ball with an upward velocity of 65 feet per second, and her foot meets the ball 1 foot off the ground. The quadratic function h=16tsquared + 65t + 1 represe      Log On


   

Question 812162: A goalie kicks a soccer ball with an upward velocity of 65 feet per second, and her foot meets the ball 1 foot off the ground. The quadratic function h=16tsquared + 65t + 1 represents the height of the ball h in feet after t seconds. Approximately how long is the ball in the air?
Found 2 solutions by richwmiller, brysca:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You have the wrong formula
h=-16t^2 + 65t + 1
set it to 0 for 0 height
0 = -16 t^2+65 t+1
t = 4.0778 about 4 seconds

Answer by brysca(112) About Me  (Show Source):
You can put this solution on YOUR website!
This relates to the physics equation, Y=Yo+Vot+.5at^2
This equation is not factorable, so there is no other option to use except through the quadratic formula. (I think the problem may have been typed wrong, so I am making the "a" value -16 instead of 16.)
The equation can be re-written as this:
-16t^2+65t+1=0
a=-16
b=65
c=1
Now, we use the quadratic formula, which is
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
and plug in the respective variables.
t+=+%28-65+%2B-+sqrt%28+65%5E2-4%2A-16%2A1%29%29%2F%282%2A-16%29+
This simplifes to +%28-65+%2B-+sqrt%284289%29%29%2F-32+
Nothing can be simplified in the above equation so if you plug in the numbers, your answer should be
t=-0.0153267912541177, 4.07782679125412 because there's always two answers in quadratics.
Time obviously cannot be negative so the answer you are left with is t=4.07782679125412.
Or you can just say t equals about 4 seconds.
Cheers,
-Bryan