Hitting a Baseball: Solving Physics Problem

[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?

Homework Equations

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?

 

[AnkhUNC]

Nevermind, solved.

 

[Moetasim]

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.