SOLUTION: A soccer ball is kicked straight up with an initial velocity of 32 ft. per second. Its height above the earth is given by s (t) = -16t^2 + 32t, where,‘s’ is the height in ft. at an

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Question 211669: A soccer ball is kicked straight up with an initial velocity of 32 ft. per second. Its height above the earth is given by s (t) = -16t^2 + 32t, where,‘s’ is the height in ft. at any time, ‘t’ seconds.
What is the maximum height reached by the ball?
How long after it was thrown up the ball reaches its maximum height?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
s(t) = -16t^2 + 32t
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One way to find the time to max height is to solve for the 2 times when the ball is at ground level, s = 0, and divide by 2. It takes the same amount of time to ascend as to descend.
-16t^2 + 32t = 0
t(-16t + 32) = 0
t = 0 (at the start)
t = 2 (at impact)
The time at max height is 1 second.
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For max height:
s(1) = -16*1 + 32*1
s max = 16 feet