SOLUTION: a ball is thrown into the air from a height of 3 feet with an initial velocity of 20 feet per second and is caught at a height of 6 feet. Find the maximum height of the ball and ho

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Question 387379: a ball is thrown into the air from a height of 3 feet with an initial velocity of 20 feet per second and is caught at a height of 6 feet. Find the maximum height of the ball and how long it takes to hit the ground.
Answer by stanbon(75887) (Show Source):
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a ball is thrown into the air from a height of 3 feet with an initial velocity of 20 feet per second and is caught at a height of 6 feet. Find the maximum height of the ball and how long it takes to hit the ground.
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h(t) = -16t^2+20t+3
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Max height occurs when t = -b/(2a) = -20/(2*-16) = 5/8 sec.
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Height at that time: h(5/8) = 9.25 ft.
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Ground time:
Solve -16t^2+20t+3 = 0 for "t":
t = [-20 +- sqrt(20^2-4*-16*3)]/-32
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t = [-20 - sqrt(592)]/-32
t = 1.3853 seconds
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Cheers,
Stan H.