SOLUTION: A ball is thrown upward into the air with an initial velocity of 128ft/s. The equation h(t)= -16t2 + 128t. Find the maximum height that the ball will attain?

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Question 149814: A ball is thrown upward into the air with an initial velocity of 128ft/s. The equation h(t)= -16t2 + 128t. Find the maximum height that the ball will attain?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the maximum height, h, of the ball:
h%28t%29+=+-16t%5E2%2B128t This quadratic equation represents a downward-opening parabola. The maximum value of the indepedent variable (that's h in this case) occurs at the vertex of the parabola. The t-coordinate of the vertex is found by:
t+=+%28-b%29%2F2a where a = -16 and b = 128, so...
t+=+%28-128%29%2F2%28-16%29
t+=+%28-128%29%2F%28-32%29
t+=+4 The maximum height is attained at t = 4 seconds.
To find the height at this time, substitute t = 4 into the given equation and solve for h.
h%284%29+=+-16%284%29%5E2%2B128%284%29
h%284%29+=+-256%2B512
h%284%29+=+256feet. This is the maximum height attained by the ball.