Parabolic trajectories are actually elliptical orbits

Deriving the parameters of the elliptical orbit of a projectile, and showing that this orbit is equivalent to the well-known parabolic trajectory in the short-range limit.
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #dynamics #projectile #mechanics #orbit #kepler #angularmomentum #energy #visviva #ellipse #parabola #trajectory #keplerslaws #taylorseries #calculus #differentiation #trigonometry #chainrule #physicsproblems #maths #math #science #education

[@Nxck2440]

This is really cool, I knew that orbits are elliptical but never made the connection that projectile motion is mathematically identical to an orbit (just one that happens to hit the planet again!)

[@DrBenYelverton]

I'd been thinking for a while that they must be equivalent, but hadn't worked through all the details until I made this video. It was satisfying when that familiar parabolic expression appeared!

[@cinephilia_3099]

Very nicely done..Thanks!

[@DrBenYelverton]

Thank you!

[@pjmoran42]

Crap. So all these years I've been aiming my bombs at the wrong point.

[@DrBenYelverton]

Well, at least you'll know for next time!

[@mxminecraft9410]

Can you please make a video on projectile motion on inclined plane.

[@DrBenYelverton]

Good idea, will add this to my to-do list.

[@mxminecraft9410]

@@DrBenYelverton Thx

[@MissPiggyM976]

Very interesting, thanks !

[@DrBenYelverton]

Thanks, glad to hear it!

[@mxminecraft9410]

Also in this situation what will be the trajectory of particle with escape velocity . Will there be some special feature for that

[@DrBenYelverton]

Great question! The escape velocity is such that u² = 2GM/R; from the vis-viva equation (at 4:12) this gives 1/a = 0, in other words the semi-major axis becomes infinite. This makes physical sense because at the escape velocity the projectile is no longer gravitationally bound to the Earth. The orbit is no longer closed and in fact becomes a parabola.

[@singhvijay124]

volume coming is little low.