Question

after 1 second the ball is 76 feet in the air: after 2 seconds it is 144 feet in the air. Find the height of the function. h(x)= ?

Answer 1

General equation for height, h
h = ut + 0.5gt^2

at t=1s, h = 76 feet
76 = u*1 + 0.5*a*1^2
76 = u + 0.5a

at t=2s, h = 144 feet
144 = u*2 + 0.5*a*2^2
144 = 2u + 2a
72 = u + a

Subtract 2 equations
0.5a = -4
a = -8
u = 80

So the equation,
h(x) = 80t + 0.5*(-8) t^2
h(x) = 80t - 4t^2