Help Finding path of a particle with an intial position and initial velocity

[ezedvin1]

Hi everyone,

I am having trouble finding the answer to a homework problem. I don't seem to understand what the question is exactly asking for. The problem is:

find the path of a particle with an initial position 10e_r + 1.0e_ϴ and an initial velocity 0.1e_r + 0.8e_ϴ

 

[ppfn]

Have you considered using the kinematics for cylindrical coordinates?

 

[ezedvin1]

the equations I am thinking about using are

Cylindrical coordinates: r, ∅, z
x=rcos∅ y=rsin∅

Spherical Coordinates: r, θ, ∅
x=rsinθcos∅ y=rsinθsin∅ z=rcosθ

I also know an equation for velocity as v=$\dot{r}$e_r + r$\dot{θ}$e_θ

I'm still very confused as to what to do with all these equations to find the path of the particle. Please Help.

 

[ppfn]

Those equations look like they are for converting from Cartesian coordinates to cylindrical / spherical coordinates.

Try looking around in your book for the kinematic equations in cylindrical / spherical form. If they aren't in your book you could try going to this link

en.wikipedia.org/wiki/Equations_of_motion

and try looking for them by Crtl+F and typing in what you're looking for.

I haven't ever worked with those coordinate systems and kinematic equations before, otherwise I would be more helpful.

 

[paranormal]

Hi there,

It looks like the question is asking you to find the path of a particle based on its initial position and velocity. In order to do this, you will need to use the equations of motion, specifically the equations for position and velocity in polar coordinates. The initial position and velocity given in the problem are in polar form, so make sure to use the correct equations for this type of coordinate system.

First, you will need to convert the initial position and velocity from polar coordinates to Cartesian coordinates. This can be done using the equations:

x = rcosϴ
y = rsinϴ

where r is the distance from the origin and ϴ is the angle from the positive x-axis.

Once you have converted the initial position and velocity to Cartesian coordinates, you can use the equations of motion to find the path of the particle. These equations are:

x(t) = x0 + v0x*t + 0.5*ax*t^2
y(t) = y0 + v0y*t + 0.5*ay*t^2

where x0 and y0 are the initial x and y positions, v0x and v0y are the initial x and y velocities, and ax and ay are the x and y components of acceleration.

Using these equations, you can plug in the initial position and velocity values to find the path of the particle at any given time t. I hope this helps you solve your homework problem. Good luck!