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?
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?
Answers
Reiny
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
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