A particle moves with its position given by x=cos6t and y=sint , where positions are given in feet from the origin and time t is in seconds.
Find the speed of the particle.
I took the derivative of each equation and then plugged it into the formula velocity=sqrt((dx/dt)^2+(dy/dt)^2).
I got ((-6sin6t)^2+cost^2)^(1/2)ft/s for the answer, but that is incorrect.
Am I going about this the wrong way?
You can see the velocity vector very clearly:
The restriction on displacement on either components are and
Velocities of each component are and
The object moves in harmonic motion following an elliptic path, where and . and are frequency and phase angle, respectively.
If you are interested in find time in relation to and , you have a lot of work to do. You must find the relation between and expressed in , where , which will involve ODE.
That's all, I have nothing more to give. Good luck!