Globular clusters cylindrical polar coordinates

[duck78]

Homework Statement

Two globular clusters A and B have cylindrical polar coordinates relative to the centre of the galaxy (r, z, Ø) given by A = (5,2,15°) and B= (4.6,65°), where the r and z coordinates are in kiloparsecs.

Homework Equations

Find a and b the position vectors of each globular cluster relative to the centre of the galaxy, in terms of the cartesian unit vectors i, j, k.

Hence find the vector displacement of B relative to A and the separation in kiloparsecs of the globular clusters

The Attempt at a Solution

Im lost and am not sure where to start.

 

[jbsteele]

I understand that the polar coordinate equations must be converted to cartesian but am not sure how to go about it. Any help would be greatly appreciated!

 

[kerimek]

I would first clarify any confusion or uncertainties about the problem. I would ask for more information, such as the orientation and direction of the cylindrical polar coordinates, as well as any assumptions or equations that should be used to solve the problem. I would also make sure to understand the definitions and units of r, z, and Ø, as well as the significance of the given values for A and B.

Once all the necessary information is gathered, I would approach the problem by converting the cylindrical polar coordinates into Cartesian coordinates, using the equations r = √(x^2 + y^2), z = z, and Ø = arctan(y/x). This would give the position vectors for A and B, which can then be used to find the vector displacement of B relative to A.

To find the separation in kiloparsecs, I would use the distance formula d = √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2), where (x1,y1,z1) and (x2,y2,z2) are the coordinates of A and B, respectively. This would give the separation between the two globular clusters in kiloparsecs.

In conclusion, to solve this problem, I would first clarify any uncertainties and gather all the necessary information, then use the appropriate equations to convert the cylindrical polar coordinates to Cartesian coordinates, and finally use the distance formula to find the vector displacement and separation between the globular clusters.