Use Conservation of energy to solve projectile motion

Oct 2019


I’m working on this homework problem and am having trouble finding a way to explicitly solve for initial velocity. I got a hint from my professor that the final point should be at the top of the parabola, but I may have misunderstood him. We solved this using kinematics when we were on kinematics, but I am struggling to solve this using energy and the parabolic free fall range formula.

Using energy, and setting final at the top of the parabola, I get Ki = Ugf
Because this is projectile motion and x-y components are independent, I am subbing (vcos)^2 + (vsin)^2 into v for Ki. This is where I am stuck.

Any help is very much appreciated!
Last edited:


PHF Helper
Jun 2010
Morristown, NJ USA
Start by determining the initial vertical component of velocity that allows the ball to just clear the peak of the roof of the house (using the formula derived from the first image you posted). Then determine the time in the air for the ball to rise to the height of the peak of the roof and fall back down. From this you should now be able to calculate the horizontal component of velocity. Post back with your work and we'll check it for you.
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