A baseball is thrown from the roof of a building and modeled by the function below where h is the height and t is the time in seconds. How long does it take the baseball to reach its maximum height? h=−5t2+30t+10
Answers
Given : A baseball is thrown from the roof of a building and modeled by the function below where h is the height and t is the time in seconds.
h=−5t²+30t+10
To Find : How long does it take the baseball to reach its maximum height?
Solution:
h=−5t²+30t+10
dh/dt = -10t + 30
dh/dt = 0
=> -10t + 30 = 0
=> t = 3
d²h/dt² = - 10 < 0
Hence maximum height at t = 3
it takes 3 secs to reach max height
max height :
h=−5t²+30t+10
t = 3
=> h = - 5(3)² + 30(3) + 10
=> h = -45 + 90 + 10
=> h = 55
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