How Do You Describe the Path of an Object Given Its Coordinates Over Time?

[Stressed out]

Motion in two dimensions! Help!

Homework Statement

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.

Homework Equations

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

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).

 

[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.

 

[Stressed out]

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.

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?

 

[lendav_rott]

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

 

[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 ?

 

[HallsofIvy]

Homework Statement

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),

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?

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.

Homework Equations

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

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).

 

[Stressed out]

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?

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.)