Question 176381: Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150ft/sec from a height of 5 ft.
If an object is given an initial velocity of v feet/second from a height of s feet, then its height S after t seconds is given by the formula
S= -16t^2 + vt + s.
a. Use the formula to determine how long it takes the ball to return to earth.
b. Estimate the maximum height reached by the ball.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150ft/sec from a height of 5 ft.
If an object is given an initial velocity of v feet/second from a height of s feet, then its height S after t seconds is given by the formula
S(t) = -16t^2 + vt + s.
a. Use the formula to determine how long it takes the ball to return to earth.
At earth its height will be zero.
-16t^2 + 150t + 5 = 0
t = [-150 +- sqrt(150^2 - 4*-16*5)]/-32
t = [-150 +- sqrt(22820)]/-32
Positive solution:
t = [-150 - 151.063]/-32
t = 9.408 seconds
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b. Estimate the maximum height reached by the ball.
Max occurs when t = -b/2a = -150/[-32] = 4.6875 seconds
S(4.6875) = -16(4.6875)^2 + 150(4.6875) + 5 = 356.56 ft.
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Cheers,
Stan H.
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