How Does Conservation of Energy Determine Initial Speed in Projectile Motion?

AI Thread Summary
The discussion focuses on solving for the initial speed of a stone thrown upward at a 53-degree angle, reaching a maximum height of 24 meters, using the Conservation of Energy principle. The equation derived is mgh = 1/2 mv^2, where the mass cancels out, indicating it is unnecessary for the calculation. The approach is confirmed correct despite initial confusion about the missing mass. The key takeaway is that energy conservation allows for solving projectile motion problems without needing to know the object's mass. Understanding this principle simplifies the analysis of projectile motion.
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A stone is thrown upward at an angle of 53 degrees above the horizontal. Its maximum height above the release point is 24m. What was the stone's initial speed?
Assume any effects of air resistance are negligible.

This problem is to be solved using Conservation of Energy.

Since there is no external force nor non-conservative forces present, this is just the change in mechanical energy.

Uf + Kf = Ui + Ki
mgh + 0 = 0 + 1/2 mv^2
=mgh = 1/2 mv^2
where y = 0 at the horizontal.

I got stuck because the mass of the stone is not given. Is my approach wrong?
 
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Divide both sides of your last line by the mass. Notice that the mass cancels out of the equation! You don't need to know it.
 
Doh!
Thanks for pointing that out.
 

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