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

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) (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

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