Solving a Physics Problem: Will the Ball Clear the Fence?

[Jeff B]

okay well I know this is a fairly simple problem, but I guess my brain isn't it gear today. I'm having trouble figuring this out.

A batter hits a pitched ball when the center of the ball is 1.22 m above the ground. The ball leaves the bat at an angle of 45 degrees with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 107 m.
(a) Does the ball clear a 7.32 m-high fence that is 97.5 m horizontally from the launch point? (b) What is the distance between the top of the fence and the center of the ball when the ball reaches the fence?





thanks,

Jeff

 

[Doc Al]

OK. Where are you getting stuck? Show your work to get help. (Start by writing the equations describing the vertical and horizontal position of the ball as a function of time.)

 

[quicknote]

I would approach this problem by first breaking it down into smaller, more manageable parts. Let's start with the given information: the ball is launched at an angle of 45 degrees and has a horizontal range of 107 m. This means that the ball will travel 107 m horizontally before returning to its original height.

Next, we need to consider the dimensions of the fence. The fence is 7.32 m high and 97.5 m away from the launch point. This means that the ball needs to clear a vertical distance of 7.32 m and a horizontal distance of 97.5 m to clear the fence.

Now, let's use some physics principles to solve this problem. We know that the ball's motion can be broken down into horizontal and vertical components. The horizontal component of the ball's motion is unaffected by gravity, so it will travel at a constant velocity of 107 m/s.

The vertical component, however, is affected by gravity and will follow a parabolic path. We can use the equation y = y0 + v0yt + 1/2at^2 to determine the height of the ball at any given point in time. In this case, we are interested in the height of the ball when it reaches the fence, so we can set y = 7.32 m and solve for t.

Once we have the time, we can plug it into the equation for horizontal distance, x = x0 + v0xt, to determine the distance between the launch point and the fence when the ball reaches the fence.

To answer part (a) of the question, we can compare the calculated distance to the actual distance of 97.5 m. If the calculated distance is greater than 97.5 m, then the ball will clear the fence.

For part (b), we can use the same equations to determine the height of the ball when it reaches the fence and subtract it from the height of the fence to determine the distance between the top of the fence and the center of the ball.

In conclusion, by breaking down the problem and using physics principles and equations, we can determine whether the ball will clear the fence and the distance between the top of the fence and the center of the ball when it reaches the fence. I hope this helps you with your problem-solving process. Keep practicing and don't be discouraged if you struggle with a problem, even the