SOLUTION: Maximum height. If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t)= -16

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Question 47784: Maximum height. If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t)= -16t^2 + 32t where t is time in seconds. Graph this parabola for 0 =< t =< 2. What is the maximum height reached by the ball?


Thank you
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
s%28t%29=+-16t%5E2+%2B+32t
At t = 0, s%280%29+=+0 because the height is zero.
At t+=+2, s%28t%29+=+0 also because
s%282%29=+-16%2A%282%5E2%29+%2B+32%2A2
s%282%29=+-64+%2B+64
s%282%29+=+0
In 2 sec the ball lands back on the ground.
The max height is midway between 0 and 2, which is 1,
so in 1 sec the ball reaches its max height, and the
max height is
s%281%29=+-16%2A%281%5E2%29+%2B+32%2A1
s%281%29+=+-16+%2B+32
s%281%29+=+16
The max height is 16 feet
+graph%28+300%2C+300%2C+-1%2C+4%2C+-2%2C+20%2C+-16%2A%28x%5E2%29+%2B+32x%29+