# Analyzing Projectile Motion via Circular Motion approach

I'm a high school physics student, and I've been puzzling over how one can derive the equations regarding projectile motion geometrically. To do so, I began thinking of projectile motion in terms of circular motion, for 2 main reasons, including:

• All projectile motion problems in high school physics involve perfectly symmetric parabolas, and can thus be interpreted to be part of a circle; a circular segment.
• At just the right theta & resultant velocity, a projectile can be launched such that begins orbiting the earth, or whatever planetary body the problem concerns, thus resulting in a form of circular motion

Exactly why may this be useful? Well, the vertical & horizontal displacement could be found much easier (in some cases), using simple geometry.

Question: Exactly how can one derive the equations for projectile motion geometrically, via the same means we approach circular motion problems?

Diagram provided below:

• "Well, the vertical & horizontal displacement could be found much easier (in some cases), using simple geometry." What cases are you thinking about? Projectile motion is parabolic, which is NOT easily handled with circles. Dec 9, 2017 at 4:30
• "high school physics [problems] involve perfectly symmetric parabolas", typically without air resistance. Dec 9, 2017 at 4:36
• Your first bullet point is incorrect. A parabola is a conic section not part of a circle; a circular segment. This invalidates the rest of your reasoning. Dec 9, 2017 at 5:32
• Most high school physics problems deal with parabolas in a two dimensional space, which is why I believe it would be much easier to analyze it as a segment of a circle. Dec 9, 2017 at 15:33
• @DarkRunner Parabolas in two dimensional space are not circular segments though. They have different shapes. Why use something wrong when we can use the easier parabola?
– JMac
Dec 9, 2017 at 18:54

" Exactly why may this be useful? Well, the vertical & horizontal displacement could be found much easier (in some cases), using simple geometry. "

Well,in most of the high school problems,the only parameters given to you are angle theta and initial velocity u. I don't get your point of calculating displacement easily.

Through my understanding of your question, basically you want to say that we can consider parabola as a segment of circle.

Well,that would not be completely wrong but I want to add that a segment of circle too is only roughly parabolic.

According to me,it would be tougher actually.....

• "Well,that would not be completely wrong." It would be completely wrong. Most parabolas are not even close to a circular arc.
– Chris
Dec 9, 2017 at 22:22