Posted by **Elizabeth** on Sunday, March 31, 2013 at 6:18pm.

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?

- Algebra -
**Reiny**, Sunday, March 31, 2013 at 7:07pm
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

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