Trajectory of a Baseball: Will it Clear the Fence?

In summary, the conversation is about a student struggling with a physics problem and seeking help from a study partner. The problem involves calculating the horizontal range of a ball hit by a batter, and determining if it will clear a fence. The student makes a mistake in their calculations, but corrects it with the help of a listener.
  • #1
RoganSarine
47
0
Now I'm seriously just tired and can't get these, but I don't know why this is wrong at all. This would help if I had a study partner in my physics class (to bounce ideas off of), but no one else in my class is overly strong in the subject.

Homework Statement


A batter hits a pitched ball when the center of the ball is 1.22m above the ground. The ball leaves the bat at an angle of 45 degress with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 107m

(a) Does the ball clear a 7.32m high fence that is 97,5 n horizontally from the launch point? (b) At the fence, what is the distance between the fence top and the ball center?


Homework Equations


y = (tan theta)x - (g(x^2))/(2(vicos45)^2)

R = (2Vi^2/g)(Sin 2 Theta)



The Attempt at a Solution



107 = (2Vo^2/g) * Sin 2(45)
107 * g = 2Vo^2 * 1
1048.6 / 2 = Vo^2
524.3 = Vo^2
22.89 = vo^2

y = (tan 45)(97.5) - (9.8(97.5)^2) / ((2)(-524.3)(cos45)^2)

y = 97.5 - 177.58

y = -80

The ball clears the fence, so why am I getting -80 for the y coordinate?

Okay, how about this... Let's try using basic kinematics

vix = d/t

t = d/vix
t = 97.5/(22.89cos45)
t = 6.023

d = Viy(t) + .5(g)t^2
d = 22.89sin45(6.023) + .5(-9.8)(6.023)^2
d = 97 - 177.7
d = -80

Why am I getting -80 as my displacement? It's supposed to clear the fence. I had to obviously have done something wrong when calculating the Vi in the range.
 
Physics news on Phys.org
  • #2
RoganSarine said:
R = (2Vi^2/g)(Sin 2 Theta)
Your range formula is incorrect.
 
  • #3
Yeah, after I went to bed I realized that there was a random 2 that I forgot to get rid of in my Sin 2 Theta identity... Thanks for confirming it.
 

1. What factors affect the trajectory of a baseball?

The trajectory of a baseball is affected by several factors including air resistance, spin, gravity, and initial velocity. The air resistance and spin can cause the baseball to curve or change direction, while gravity pulls the ball towards the ground. The initial velocity, or speed and direction at which the ball is thrown, also plays a significant role in the trajectory.

2. How does air resistance affect the trajectory of a baseball?

Air resistance, also known as drag, affects the trajectory of a baseball by slowing it down as it travels through the air. This can cause the ball to drop more quickly than it would without air resistance, resulting in a steeper trajectory. Air resistance can also cause the ball to curve or change direction depending on the spin of the ball.

3. How does spin affect the trajectory of a baseball?

Spin is another important factor in the trajectory of a baseball. A ball with topspin will tend to drop more quickly, while a ball with backspin will tend to stay in the air longer. Spin can also cause the ball to curve, depending on the direction and speed of the spin. This is why pitchers often use different types of pitches, such as a curveball or slider, to create a variety of trajectories.

4. How does the weight of a baseball impact its trajectory?

The weight of a baseball can impact its trajectory in a few ways. A heavier ball will require more force to throw, resulting in a higher initial velocity and a flatter trajectory. However, a heavier ball may also be more affected by air resistance and gravity, causing it to drop more quickly. Major League Baseballs are carefully regulated to ensure they are within a specific weight range to maintain consistency in gameplay.

5. How does altitude affect the trajectory of a baseball?

Air density, which is affected by altitude, can impact the trajectory of a baseball. At higher altitudes, the air is less dense, meaning there is less air resistance to slow down the ball. This can result in longer distances for hits and pitches. However, the lower air density also means there is less lift force on the ball, causing it to drop more quickly. This is why home runs are more common in stadiums at higher altitudes, such as Denver's Coors Field.

Similar threads

Projectile Motion Problem: Kicking a soccer ball over a fence
    • Introductory Physics Homework Help
Replies
11
Views
949
Needing some help about time of flight of a launched ball/horiz range
    • Introductory Physics Homework Help
Replies
6
Views
2K
Calculating Time for Ball to Reach Fence Plane
    • Introductory Physics Homework Help
Replies
1
Views
986
Kinematics: baseball toss with an angle provided
    • Introductory Physics Homework Help
Replies
3
Views
3K
Need help finding final speed of a projectile
    • Introductory Physics Homework Help
Replies
2
Views
1K
Ball is thrown at the edge of the roof of a building
    • Introductory Physics Homework Help
Replies
31
Views
3K
Would the baseball clear the fence- projectile motion
    • Introductory Physics Homework Help
Replies
1
Views
5K
Solving Ball Clearing Fence: Does It Go Over?
    • Introductory Physics Homework Help
Replies
4
Views
3K
Ball trajectory velocity and displacement vectors
    • Introductory Physics Homework Help
Replies
13
Views
2K
How Can I Find the Initial Velocity of a Ball Based on Angle and Window Height?
    • Introductory Physics Homework Help
Replies
3
Views
959

Hot Threads

Recent Insights

Back
Top