Answer:
Maximum height, h(t) = 95 meters
Explanation:
A ball travels on a parabolic path in which the height (in feet) is given by :
[tex]h(t)=-16t^2+64t+31[/tex].............(1)
Where
t is the time after launch
We need to find the maximum height of the ball in feet. For maximum height,
[tex]\dfrac{dh(t)}{dt}=0[/tex]
[tex]\dfrac{d(-16t^2+64t+31)}{dt}=0[/tex]
[tex]-32t+64=0[/tex]
t = 2
Put the value of t in equation (1) as :
[tex]h(t)=-16(2)^2+64(2)+31[/tex]
h(t) = 95 meters
So, the maximum height of the ball is 95 meters. Hence, this is the required solution.
