Conservation of energy of a baseball problem

AI Thread Summary
The problem involves calculating the speed of a baseball just before it strikes the ground using conservation of energy principles, with an initial height of 21.2 meters and an initial velocity of 10.7 m/s at a 54.4-degree angle. The relevant equations include potential energy (PE = mgh) and kinetic energy (KE = 1/2 mv^2), leading to the conservation of mechanical energy equation KEi + PEi = KEf + PEf. The discussion highlights that the mass of the baseball cancels out in the calculations, allowing the speed to be determined without knowing the mass. The problem also emphasizes understanding the factors that affect mechanical energy.
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Homework Statement


A baseball is thrown from the roof of a building of height 21.2m with an initial velocity of magnitude 10.7 m/s and directed at an angle of 54.4 degrees above the horizontal.

a. What is the speed of the ball just before it strikes the ground? Use energy methods and ignore air resistance.

b.What is the answer for part (A) if the initial velocity is at an angle of 54.4 below the horizontal?

Homework Equations


PE=mgh
KE=1/2mv^2

KEi+PEi=KEf+PEf

The Attempt at a Solution


I'm not exactly sure where to begin. I'm thinking I have to find the max height the ball achieves using projectile motion methods then use conservation of energy?
 
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You can find the answer using just the equations you cited. If you are puzzled, try see which of the four terms in the last equation (i.e. conservation of mechanical energy) you know and if that will let you determine the value you seek. Besides doing the actual calculation the problem is also meant to make you think about what mechanical energy depends on and what it (surprisingly, maybe) does not depend on.
 
Ok. so PEf is going to be zero, correct? and KEi is zero because the ball starts from rest. But I'm not given the mass, how can I figure out v? Do they cancel because they are constant?
 
The mass m that enters the four terms are all the same mass, so you are right, it cancels.
 
I got it, thanks! I appreciate the help.
 

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