Question

A ball is propelled straight up with an initial velocity of 250ft/sec in a vacuum with no air resistance. How high will it go?

Answer 1

acceleration of gravity is -32 ft/sec^2
velocity function is : -32t + v, where v is initial velocity
v = 250
v(t) = -32t + 250
height function is: -16t^2 + 250t +H, where H is initial height
H = 0
h(t) = -16t^2 +250t
maximize h(t) by finding vertex
t = -b/2a = -250/-32 = 125/16
max height = -16*(125/16)^2 + 250*(125/16)