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

• Stressed out
In summary, 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). To solve this problem, the student attempted to solve all parts except for part d. After plotting x and y coordinates for different values of time, they found that the value of v is not provided. They tried varying v values, but found no significant change. The student then tried plotting x and y coordinates for different values of x^2+y^2, which yielded the graph shown.
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).

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.

lendav_rott said:
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?

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

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 ?

Stressed out said:

## 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).

1 person
HallsofIvy said:
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.)

## What is motion in two dimensions?

Motion in two dimensions refers to the movement of an object in both the x and y directions simultaneously. This means that the object is not just moving in a straight line, but also has a vertical component to its motion.

## What is the difference between motion in one dimension and two dimensions?

Motion in one dimension only involves movement in a single direction, usually represented by the x-axis. In two dimensions, the object is moving in both the x and y directions, making it more complex to analyze.

## What is the formula for calculating the displacement in two dimensions?

The formula for calculating displacement in two dimensions is Δr = √(Δx² + Δy²), where Δx and Δy are the changes in the x and y directions respectively. This formula uses the Pythagorean theorem to calculate the total distance traveled by the object.

## How is velocity calculated in two dimensions?

In two dimensions, velocity is calculated by dividing the total displacement by the total time taken. This gives the average velocity of the object over the entire motion. To calculate instantaneous velocity, the derivative of the position function with respect to time can be used.

## What is projectile motion?

Projectile motion is a special type of motion in two dimensions where an object is launched into the air and moves in a curved path due to both its horizontal and vertical velocities. This type of motion is affected by gravity, air resistance, and initial launch angle and velocity.

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