Hitting a Baseball: Solving Physics Problem

• AnkhUNC
In summary, the conversation is about a batter hitting a baseball at a certain angle and height, and determining if it will clear a fence that is a certain distance away. The solution involves calculating the initial velocity and using equations to find the time and height of the ball.
AnkhUNC
[SOLVED] Hitting a baseball

Homework Statement

A batter hits a pitched ball when the center of the ball is 1.37 m above the ground.The ball leaves the bat at an angle of 45° with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 106 m. (a) Does the ball clear a 8.40-m-high fence that is 96.0 m horizontally from the launch point? (b) At the fence, what is the distance between the fence top and the ball center?

The Attempt at a Solution

So for v0 I get sqrt(9.8*106/1) = 32.38209382

So to find out when its over the fence I do 96/t*cos(45) = 4.192579478

So I then plug this into y = y0+(v0*sin(45))t - 1/2 g(t^2) = 11.23915888 which means it clears the fence but,

This minus 8.4 = 2.84 but its saying that this answer is incorrect. Anyone see where I'm going wrong?

Nevermind, solved.

I would first like to commend you on your attempt to solve this physics problem. It is clear that you have a good understanding of the equations involved and have correctly identified the initial velocity and launch angle of the ball.

However, I believe there may be a mistake in your calculation for the time it takes for the ball to reach the fence. When solving for time, we should use the horizontal distance of 96 m, not the vertical distance of 8.4 m. This gives a time of approximately 2.97 seconds, which when plugged into the equation for vertical position, gives a height of 10.71 m. This means that the ball does clear the fence, with a margin of 2.31 m.

Additionally, for part (b) of the problem, we can use the same time of 2.97 seconds to calculate the horizontal distance the ball has traveled. This gives a distance of approximately 83.89 m, which when subtracted from the total horizontal distance of 96 m, gives a distance of 12.11 m between the fence top and the ball center.

In conclusion, I believe your initial approach was correct, but there may have been a mistake in your calculation for time. I hope this helps in solving the problem.

1. How does the speed of the baseball affect the distance it travels when hit?

The speed of the baseball is directly related to the distance it will travel when hit. According to the laws of physics, the greater the initial speed of the object, the farther it will travel. This is because a higher initial speed means the ball has more kinetic energy, which allows it to travel a greater distance before slowing down due to air resistance.

2. Does the angle at which the bat hits the ball affect its trajectory?

Yes, the angle at which the bat hits the ball can greatly affect its trajectory. This is because the angle of impact determines the direction of the ball's initial velocity. If the bat hits the ball at an angle, the ball will have a curved trajectory. The optimal angle for hitting a baseball is typically between 25-35 degrees.

3. How does the weight of the bat affect the force of the impact?

The weight of the bat does have an impact on the force at which it hits the ball. According to Newton's Second Law of Motion, force is equal to mass times acceleration. Therefore, a heavier bat will result in a greater force of impact on the ball, which can lead to a higher exit velocity and longer distance traveled.

4. What factors affect the trajectory of a baseball after it is hit?

Several factors can affect the trajectory of a baseball after it is hit, including the initial speed of the ball, the angle at which it is hit, and the effects of air resistance. The spin of the ball can also play a role in its trajectory, as well as any external forces such as wind or gravity.

5. How does the density of the bat affect the distance the ball travels?

The density of the bat can have a significant impact on the distance the ball travels. A denser bat will transfer more energy to the ball upon impact, resulting in a higher exit velocity and longer distance traveled. However, there is a limit to how much density can improve performance, as a bat that is too heavy will be difficult to swing with enough speed to make a difference.

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