Problema Solution
If a football is kicked straight up with an initial velocity of 96 ft/sec from a height of 6 ft, then its height above the earth is a function of time given by h(t)=-16t^2+96t+6. What is the maximum height reached by the ball?
Answer provided by our tutors
We need to find the maximum of the parabolic function:
h(t)=-16t^2+96t+6
Since the quotient in front of t^2 is -16<0 the function has maximum:
h max = c - b^2/(4a), where a = -16, b = 96, c = 6
h max = 6 - 96^2/(4*(-16))
h max = 150
The maximum height reached by the ball is 150 ft.
click here to see the graph of the function y = -16x^2+96x+6
