Maximum Height

1. Jan 22, 2009

hthorne21

A baseball is hit deep to center field. The vertical position from home plate of the ball with respect to time is described by:
v(t) = -20t2 + 103.5t +5 in feet above home plate
The horizontal distance from home plate is described by:
h(t) = 84.32t in feet where t is in seconds
HINT: The orgin is at home plate, with the vertical axis going straight up from home plate and the horizontal axis heading out towards center field, along the flight path of the base ball
FIND:
a) the maximum height, in feet, that the ball achieves.

b) Assuming level terrain, does the ball clear the 12 foot wall located 420 feet from home plate for a home run?

2. Jan 22, 2009

LowlyPion

How would you expect to start?

3. Jan 22, 2009

hthorne21

take the derivative of v(t) the set it equal zero to get t=2.588
then what do you do with the 2.588, put it in the orginal function or do you plug it into the h(t) function

4. Jan 22, 2009

LowlyPion

To determine max height, plug it in h(t).

EDIT: Sorry I misread the original. h(t) here is the horizontal distance equation.

Use V(t) equation.

Last edited: Jan 22, 2009
5. Jan 22, 2009

LowlyPion

For b) determine when the ball arrives at the wall from your h(t) equation. Then plug that time into a height equation. V(t)

Last edited: Jan 22, 2009