SOLUTION: thanks so much for helping me, guys!...i am almost finished with this unit, but unfortunately i am stumped again. imagine you are serving a volleyball underhanded. suppose you h

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Question 65416: thanks so much for helping me, guys!...i am almost finished with this unit, but unfortunately i am stumped again. imagine you are serving a volleyball underhanded. suppose you hit the ball when it is 3 feet above the ground, and it leaves your hand with an initial upward velocity of 20 feet per second.
general formula for height: H=-1/2*gt^+vt+h where g is the acceleration due to gravity, and on the earth, equals 32ft/sec^. v is the initial upward velocity of the object and h is the initial height above the ground.
the question is: what is the maximum height that the volleyball will reach and how many seconds will it take to reach this height?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine you are serving a volleyball underhanded. suppose you hit the ball when it is 3 feet above the ground, and it leaves your hand with an initial upward velocity of 20 feet per second.
general formula for height: H=-1/2*gt^+vt+h where g is the acceleration due to gravity, and on the earth, equals 32ft/sec^. v is the initial upward velocity of the object and h is the initial height above the ground.
the question is: what is the maximum height that the volleyball will reach and how many seconds will it take to reach this height?
h=3, v=20, and g=32
The formula for height:
H=%28-1%2F2%29%2832%29t%5E2%2B%2820%29t%2B3
H=-16t%5E2%2B20t%2B3
The maximum height is the H value of the vertex.
The formula for finding the t value of the vertex is: t=-b%2F2a for a quadratic equation in this form: H=at%5E2%2Bbt%2Bc
a=-16, b=20, and c=3
t=-20%2F%282%28-16%29%29
t=20%2F32
t=.625
The maximum height H, will happen when t=.625 s.
H=-16%28.625%29%5E2%2B20%28.625%29%2B3
H=-16%28.390625%29%2B20%28.625%29%2B3
H=-6.25%2B12.5%2B3
H=9.25
The Maximum height is: 9.25 ft or 9 ft 3 in
Happy Calculating!!!