Problema Solution
From 2 feet above home plate, Grady hits a baseball upward with a velocity of 36 feet per second. The height h(t)of the baseball t seconds after Grady hits it is given by h(t)=-16t^2+36t+2. Find the maximum height reached by the baseball and the time that this height is reached.
Answer provided by our tutors
we need to find the maximum value of the parabolic function
h(t)=-16t^2+36t+2
the quotient in front of t^2 is -16 < 0 thus the function has maximum equal to c - b^2/(4a) where a = -16, b = 36, c = 2
h max = 2 - 36^2/(4*(-16))
h max = 22.25 ft
lets find t such that h(t) = 22.25
-16t^2+36t+2 = 22.25
- 16t^2 + 36t - 20.25 = 0 divide both sides by -16
t^2 - 2t + 20.25/16 = 0
by solving the equation we find
t = 9/8
t = 1.125 s
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plot the graph of the function h(t)=-16t^2+36t+2 to check the solution
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the maximum height reached is 22.25 ft and the time when this heights is reached is 1.125 seconds.