# Motion in two dimensions Help!

1. Feb 18, 2014

### Stressed out

Motion in two dimensions!! Help!

1. The problem statement, all variables and given/known data

The coordinates of an object moving in the xy plane
vary with time according to the equations x =-5.00 sin (vt) and y= 4.00 - 5.00 cos (vt),
where v is a constant, x and y are in meters, and t is in seconds.
(a) Determine the components of velocity of the
object at t = 0. (b) Determine the components of
acceleration of the object at t = 0. (c) Write expressions
for the position vector, the velocity vector, and
the acceleration vector of the object at any time t > 0.
(d) Describe the path of the object in an xy plot.

2. Relevant equations

x =-5.00 sin (vt)
y= 4.00 - 5.00 cos (vt),

3. The attempt at a solution
I was able to solve all the parts of this question except part d.
I tried plotting the x y coordinates for different values of time, but the value of v is not provided. Should I consider some random value for v?
P.S: v actually has the angular velocity symbol in my book. (the abnormal w).

2. Feb 18, 2014

### lendav_rott

It is said that v is a constant, some certain angular velocity, it doesn't matter what it is. Could be pi radians/s or pi/2 radians/s or it could be 0 radians/s, it is constant.
Sinusoid is a periodic function, they want you to plot what that 1 period looks like in an xy plane, most likely.

3. Feb 18, 2014

### Stressed out

So, I can assign any value for the angular velocity and then plot the curve using x and y coordiantes from different values of time?

4. Feb 18, 2014

### lendav_rott

Yes, you can do that.
Try plotting with different values for v, see if anything significantly changes or not.

5. Feb 18, 2014

### BvU

The abnormal w is an omega, greek for big o. Big meaning long in this context. That's why they write two almost o's (they also have an omikron, small o, our current o).
In PF these are available under advanced by simply clicking ω (or Ω - but not here because that is resistance for a physicist).

A much better alternative is to use ${\#}{\#}$ \omega, \Omega, \omicron, O, o ${\#}{\#}$ to get $\omega, \Omega, \omicron, O, o$

(My 1984 $\TeX$book says there is no \omicron but now I discover it is there; but the \Omicron is not. Well, progress!)

Oh, and: look through the problem. Would you recognize x = sin t, y = cos t ? If so, what about x and y-4 in your problem ?

6. Feb 18, 2014

### HallsofIvy

Staff Emeritus
So $x= -5.00 sin(vt)$ and $y- 4.00= -5.00 cos(vt)$

What is $x^2+ (y- 4)^2$?

What is the graph of that?

7. Feb 19, 2014

### Stressed out

yES I GOT IT! oNE THING THOUGH. if I GET SUCH QUESTIONS, DO WE ALWAYS HAVE TO THEN ELIMINATE THE (t) , in order to combine the x and y?
(sorry for the caps lock part. I'm not shouting.)