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

• hthorne21
In summary: Hence, max height is 267.26 ft.In summary, to find the maximum height of a baseball hit deep to center field, we can use the vertical position equation v(t) = -20t2 + 103.5t +5 in feet above home plate and take the derivative to find the time at which the ball reaches its peak. Plugging this time into the horizontal distance equation h(t) = 84.32t, we can find the maximum height achieved by the ball. To determine if the ball clears a 12 foot wall located 420 feet from home plate for
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?

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:

## 1. What is "Ding! Deep Drive to Center: Tracking the Ball's Flight"?

"Ding! Deep Drive to Center: Tracking the Ball's Flight" is a scientific study that explores the trajectory and flight of a baseball when hit with different types of pitches.

## 2. What methods were used to track the ball's flight?

The study utilized high-speed cameras and motion tracking software to capture and analyze the movements of the ball in flight.

## 3. What were the main findings of the study?

The study found that the type of pitch thrown greatly affects the trajectory and distance of the ball, with breaking pitches causing more movement and slower pitches resulting in shorter distances.

## 4. How does this study contribute to the understanding of baseball?

This study provides valuable insights for players, coaches, and fans in understanding how different pitches can affect the outcome of a play and how to strategize accordingly.

## 5. What are the potential applications of this study?

This study can be used to improve pitching techniques and help players make more informed decisions on the field. It can also be applied in other sports that involve projectile motion and trajectory analysis, such as golf or tennis.

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