# 3-Dimensional Projectile Motion

I know in 2-dimensions, the x coordinate is represented by

$$x=v_{0}\cos{(\theta)}t,$$

and the y coodinate is represented by

$$y=-\frac{1}{2}gt^2+v_{0}\sin{(\theta)}t+h.$$

How would you calculuate the z coordinate if it was rotating around the y axis? For example; a sprinkler.

ZapperZ
Staff Emeritus
alexmcavoy@gmail.com said:
I know in 2-dimensions, the x coordinate is represented by

$$x=v_{0}\cos{(\theta)}t,$$

and the y coodinate is represented by

$$y=-\frac{1}{2}gt^2+v_{0}\sin{(\theta)}t+h.$$

How would you calculuate the z coordinate if it was rotating around the y axis? For example; a sprinkler.

I wouldn't use cartesian coordinates system if I were you.....

Zz.

dextercioby
Homework Helper
Who's rotating??

Daniel.

What would you use? Even if there was a better way, I am interested in how it would be defined in rec. coordinates.

Thanks again.

dextercioby
Homework Helper
Are u thinking of a spinning (finite size) projectile wondering through the (viscous,moving,nonisothermal,nonisobaric) atmosphere,in the nonconstant nonhomogenous gravitational field created by a rotating Earth??

Daniel.

I'm thinking of no outside forces besides gravity.

dextercioby
Homework Helper
Anyway,a spinning rigid body is typically discribed by 6 coordinates:the 3 cartesian for the CM (parametrize the body's translation) and the 3 Euler angles (parametrize the body's rotations).

Daniel.

Ok well, I haven't had a physics class before, so what I know is strictly what I have read out of a book (which isn't much). What type of physics class would I learn these types of things in?

dextercioby
Homework Helper
A college course in classical mechanics in Newtonian formulation.

Daniel.

I'm thinking of no outside forces besides gravity.

I was also wondering why I can't find a formula for kinetic energy that INCLUDES motion such as rotation or even a variable orbit??? I admit I haven't seen a classroom in 15yrs. So if anyone can update me?

I know in 2-dimensions, the x coordinate is represented by

$$x=v_{0}\cos{(\theta)}t,$$

and the y coodinate is represented by

$$y=-\frac{1}{2}gt^2+v_{0}\sin{(\theta)}t+h.$$

How would you calculuate the z coordinate if it was rotating around the y axis? For example; a sprinkler.