Find path equation and velocity/acceleration vectors for r(t)=(cos2t)i+(3sin2t)j

[jdawg]

Homework Statement

r(t) is the position of a particle in the xy plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at the given value of t.

r(t)=(cos2t)i+(3sin2t)j, t=0

Homework Equations

The Attempt at a Solution

x=cos2t y=3sin2t
x²=cos²2t y²/9=sin²2t

I'm not sure if I'm on the right track with this! Can someone please give me a push in the right direction?

 

[LCKurtz]

Homework Statement

r(t) is the position of a particle in the xy plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at the given value of t.

r(t)=(cos2t)i+(3sin2t)j, t=0

Homework Equations

The Attempt at a Solution

x=cos2t y=3sin2t
x²=cos²2t y²/9=sin²2t

I'm not sure if I'm on the right track with this! Can someone please give me a push in the right direction?

Looks good so far. What do you get if you add those last two equations? Do you recognize it?

 

[jdawg]

Ohhh thanks, figured it out! :)