Hitting a Baseball: Solving Physics Problem

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The discussion revolves around solving a physics problem related to hitting a baseball, where a batter hits a ball at a height of 1.37 m and at a 45° angle, aiming to determine if it clears an 8.40 m fence located 96 m away. The initial velocity was calculated to be approximately 32.38 m/s. The time to reach the fence was derived, leading to a height calculation of 11.24 m at that point. Although the initial calculations suggested the ball clears the fence by 2.84 m, the poster initially believed this result was incorrect but later confirmed the solution. The problem illustrates the application of projectile motion equations in a real-world scenario.
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[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?
 
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Nevermind, solved.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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