Problema Solution
A ball is thrown vertically upward. After T seconds, its height H (in feet) is given by the function. H(T)=116T-16T^2.What is the maximum height that the ball will reach?
Answer provided by our tutors
H = 116t - 16t^2
velocity = dH/dt = 116 - 32t( by differentiating height)
At max height, velocity = 0 (if you imagine a ball being thrown up you will see the parabolic motion it moves in, at its peak its velocity will be 0.)
=> 116 - 32t = 0
=> t = 3.625
Hence ball reaches max height after 3.625 seconds
At t = 3.625
H = 116*3.624 - 16*3.625^2
h = 420.5 - 210.25
H = 210.25
Max height = 210.25 feet