What are the Polar Coordinates and Speed of a Car on a Straight Road?

In summary, the problem involves a car traveling on a straight road at constant speed of 65mi/hr. At an angle of 60 degrees, the values of r (with dot above) in ft/sec and theta (with dot above) in deg/sec are to be determined. The equations used are Vr = r (with dot above), Vtheta = r*theta(with dot above), and v = sqrt(((Vr)^2)+((Vtheta)^2)). The attempt at a solution involved finding Vr using v cos theta, then using it to find Vtheta and converting it to deg/sec. However, the mistake was made of using the incorrect radius of 100ft instead of the actual radius.
  • #1
krnhseya
103
0

Homework Statement



A car P travles along a straight road with a constant speed v = 65mi/hr. At the instant when the angle theta = 60 degrees, determine the values of r (with dot above) in ft/sec and theta (with dot above) in deg/sec. (r = 100ft)

The picture has a car on highway and radius pointing diagonally from the origin which is on the field in "/" like this.

Homework Equations



Vr = r (with dot above)
Vtheta = r*theta(with dot above)
v = sqrt(((Vr)^2)+((Vtheta)^2))

The Attempt at a Solution



Vr = v cos theta and found Vr without a problem.
I tried to plug in v = 65mi/hr (converted to ft/sec) into 3rd eqn with Vr in order to find Vtheta. After that I substitude it into 2nd eqn since I know the radius. I got the theta value and converted to deg/sec from rad/sec but I am not getting answer.

What mistake have I made? :(

Thank you.
 
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  • #2
What is the position of the car relative to the origin, and what direction is it moving in?
 
  • #3
wow, i just made the stupidest mistake ever...
i JUST realized that radius is NOT 100 hahaha
sorry about that! and thank you!
 

1. What are polar coordinates of a car?

Polar coordinates are a method of determining the location of a point using its distance from a fixed point (known as the pole or origin) and its angle from a fixed reference line (known as the polar axis). In the context of a car, this means the coordinates represent the car's distance from a fixed point and the direction it is facing.

2. How are polar coordinates used in cars?

Polar coordinates are often used in navigation systems, such as GPS, to determine the position and direction of a car. They can also be used in mapping and surveying to accurately plot the location of roads and other features.

3. What is the difference between polar coordinates and Cartesian coordinates?

The main difference between polar coordinates and Cartesian coordinates is the way they represent a point in a two-dimensional space. Cartesian coordinates use the x and y axes, while polar coordinates use the distance from the origin and the angle from a reference line. In terms of a car, Cartesian coordinates would represent its position on a map, while polar coordinates would represent its distance and direction from a fixed point.

4. Can polar coordinates be converted to Cartesian coordinates?

Yes, polar coordinates can be converted to Cartesian coordinates and vice versa. There are specific equations for converting between the two coordinate systems, which involve using trigonometric functions. Many calculators and computer programs have the ability to perform these conversions.

5. How do polar coordinates affect driving?

Polar coordinates do not directly affect driving as they are mainly used for navigation and mapping purposes. However, accurate positioning and direction information provided by polar coordinates can aid in driving by helping a driver determine the shortest or most efficient route to a destination.

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