Problema Solution
A boy throws a ball vertically upwards from the top of a 80 feet building with an initial velocity of 64 feet per second. The distance s (in feet) of the ball from the ground after t seconds is given by the function, s = -16t2 + 64t + 80. Find the maximum height the ball can reach.
Answer provided by our tutors
We need to find the maximum of the parabolic function:
s = -16t^2 + 64t + 80
Since the quotient in front of t^2 is negative -16 < 0 the function has maximum:
s max = (c - b^2)/(4a), where a = -16, b = 64, c = 80
s max = (80 - 64^2)/(4*(-16))
s max = 62.75 ft
The maximum height the ball can reach is 62.75 feet.