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Final KE = Initial KE + Initial PE.

This is just conservation of energy. If all objects fall the same distance and start with the same amount of kinetic energy, then conservation of energy demands that the objects' final KE be equal.

I hope that makes sense.

Claude.

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vf^2 = vo^2cos(theta)^2 + vo^2sin(theta)^2 -2*voy*g*t + (g*t)^2

but for parabolic motion w/ the same landing height we have

0 = voyt - gt^2/2 or that voy = gt/2 or

this means

vf^2 = vo^2cos(theta)^2 + vo^2sin(theta)^2 -

vf^2 = vo^2cos(theta)^2 + vo^2sin(theta)^2 -g*t*g*t + (g*t)^2

vf^2 = vo^2cos(theta)^2 + vo^2sin(theta)^2 -(g*t)^2 + (g*t)^2

vf^2 = vo^2cos(theta)^2 + vo^2sin(theta)^2

vf^2 = vo^2(cos(theta)^2 + sin(theta)^2)

vf^2 = vo^2

KEf = KE0 assuming mass is constant

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thanks to all for the quick and informative help

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