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

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Homework Help Overview

The problem involves analyzing the flight of a baseball hit deep to center field, with a focus on its vertical and horizontal motion described by given equations. Participants are tasked with finding the maximum height of the ball and determining if it clears a wall located at a specific distance.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss starting points for solving the problem, including taking derivatives of the vertical position function to find maximum height. There is also inquiry about the appropriate use of the time value obtained from the derivative in relation to the horizontal distance function.

Discussion Status

The discussion is active with participants exploring different methods to approach the problem. Some have suggested using derivatives to find critical points, while others are clarifying the roles of the vertical and horizontal equations in the context of the problem.

Contextual Notes

Participants are working under the assumption that the terrain is level and are considering the implications of the wall's height and distance from home plate in their calculations.

hthorne21
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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?
 
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How would you expect to start?
 
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
 
hthorne21 said:
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.
 
Last edited:
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:

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