Question

A baseball player hits a baseball into the air with an initial vertical velocity of 48 feet per second from a
height of 3 feet.
8. Write an equation that gives the baseball’s height as a function of the time (in seconds) after it is hit.
9. After how many seconds does the baseball reach its maximum height?
10. What is the maximum height?

Answer 1

height = -16t^2 + 48t + 3

using Calculus,
d(height)/dt = velocity = -32t + 48
= 0 at a max of height
32t = 48
t = 48/32 = 1.5

Maximum height is reached after 1.5 seconds

that height is
-16(1.5)^2 + 48(1.5) + 3 = 39 ft

If you don't know Calculus, then you have to find the vertex of the above parabola, usually by completing the square.

A short-cut would be to find the x of the vertex by
-b/(2a) = -48/(-32) = 1.5
then subbing in just like before to the actual maximum