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A soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second. Its height above ground in feet is given by:
s(t)=-16t^2 +32t
where t is time in seconds.
I am looking for the max height of the ball, as well as when it hits the ground. My major question is this: Do I have to find c before I solve this? (ax^2 +bx+ c) Is that even necessary in this word problem?
Thank you!

Sagot :

AL2006
C is the height above the floor when it's kicked . . . zero. Gravitational acceleration reduces its speed to zero in 1 second. Average speed during that time is 1/2 (32+0) = 16 feet per second. At that average speed, it rises 16 feet to its peak. Gravity works exactly the same scenario in reverse after that. Beginning 16 ft high with zero speed, it falls 16 feet in one second, and hits the ground at 32 ft per second.
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