How Much Does Gravity Affect a Baseball's Trajectory Over 18.4 Meters?

In summary, the ball will drop 1.44 meters due to the effects of gravity by the time it reaches home plate. The horizontal and vertical components of the pitch were solved separately, with the vertical component using the equation y = y_0 + v_y t + \frac{1}{2} a t^2 and assuming a perfect pitch with v_y = 0 and y_0 = 0. The final result was -1.44 meters of drop.
  • #1
creativeone
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1. While trying out for the position of pitcher on your high school baseball team, you throw a fastball at 76.4 mi/h toward home plate, which is 18.4 m away. How far does the ball drop due to effects of gravity by the time it reaches home plate? (Ignore any effects due to air resistance and assume you throw the ball horizontally.)
2. 1. x=1/2(v0+vf)t; 2. x=v0t+1/2at^2
3. I split up the values given into a horizontal and vertical table. Since neither vertical or horizontal has time, I solved horizontal for time and got .542s. I then took that and plugged into the 2nd equation listed, and got 19.8506, which was incorrect. My vertical and horizontal table looks like the following:

Vertical- a=9.8 m/s/s, h=?, t=
Horizontal- x=18.4 m, a=0, v0=33.975 m/s, vf=33.975

Any help asap would be great thank you!
 
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  • #2
Your approach looks good. Let's say everything is correct for the horizontal component...
In the vertical component you have
[itex] y = y_0 + v_y t + \frac{1}{2} a t^2 [/itex]
You are really just interested in how much the ball is dropping so let's say [itex] y_0 = 0 [/itex] .
We'll also assume this is a perfect pitch so [itex] v_y = 0 [/itex] .

So we end up with [itex] y = \frac{1}{2} a t^2 = 0.5(-9.8)(0.542^2) = -1.44 m [/itex]
 

FAQ: How Much Does Gravity Affect a Baseball's Trajectory Over 18.4 Meters?

1. What is 2D kinematics in relation to baseball?

2D kinematics is the study of motion in two dimensions, specifically in the context of baseball. It involves analyzing the position, velocity, and acceleration of a baseball in both the horizontal and vertical dimensions.

2. How is 2D kinematics used in baseball?

2D kinematics is used in baseball to understand and improve the performance of players. By analyzing the trajectory and speed of a baseball, coaches and players can make adjustments to pitching, hitting, and fielding techniques.

3. What factors affect the 2D kinematics of a baseball?

The 2D kinematics of a baseball is affected by several factors, including the initial velocity, angle of release, air resistance, and gravity. These factors can change depending on the pitcher's throwing style, the weather conditions, and the characteristics of the baseball itself.

4. Can 2D kinematics predict the outcome of a baseball game?

While 2D kinematics can provide valuable insights into the performance of players, it cannot predict the exact outcome of a baseball game. Other variables, such as teamwork, strategy, and luck, also play a significant role in determining the outcome of a game.

5. How has technology advanced the study of 2D kinematics in baseball?

Technology has greatly advanced the study of 2D kinematics in baseball. High-speed cameras, motion capture systems, and computer algorithms can now accurately track the movement of a baseball and provide detailed data for analysis. This has allowed for more precise and in-depth understanding of the 2D kinematics involved in baseball.

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