Ding! Deep Drive to Center: Tracking the Ball's Flight

[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?

 

[LowlyPion]

How would you expect to start?

 

[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

 

[LowlyPion]

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

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.

 

[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)