# Locus Question on multiple moving objects

1. Feb 8, 2013

### Jay_

Hi,

I had a some locus questions, these are not a homework question but I was just curious as to how anyone would go about them.

Q1. Lets say there is kid walking in a circle of diameter 2 m at a speed of 1 m/s at the back of a truck. The truck is headed due east at a speed of 15 m/s. What equation would describe the locus of the head of the kid, with respect to the (stationary) ground, if we consider eastward as the x-axis?

OR

Q2. I also had one more actually, I have a cylinder of diameter 4 m, rolling down an incline that has an angle of 30 degrees. Inside the cylinder, there is an object oscillating uniformly at a speed of 10 Hz. (i.e. 10 oscillations across the diameter per second).

If we consider the incline as the x-axis, and the object oscillating about that diameter which is perpendicular to the x-axis, what would describe the locus of the oscillating object?

How do we go about finding the equation for such "superimposed motions" would trace out on a x-y plane and get an equation in terms of parametric form or as y = f(x) ?

The scale of the x-y plane is say in SI units. That is 1 unit in each of the axes is 1 m.

Last edited: Feb 8, 2013