Problema Solution
A rock it thrown from the top of a tower that is 500 feet tall. If its height above the ground can be modeled by
h(t)=-16t^2+64t+500 where h is in feet, and t is in seconds.
To the nearest tenth of a second, how long will it take the rock to reach its maximum height?
Answer provided by our tutors
the parabolic function h(t)=-16t^2+64t+500 has a negative quotient in front of t^2 (-16<0) thus the function has maximum equal to c - (b^2/(4a)), where a = -16, b = 64 and c = 500
h max = 500 - (64^2/(4(-16)))
h max = 564
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we need to find t such that h(t) = 564 that is
-16t^2+64t+500 = 564
by solving we find
t = 2 s
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the rock will reach its maximum after 2 seconds.