# Worksheet: Coordinate Systems

In this worksheet, we will practice performing vector calculations in different coordinate systems such as polar, cylindrical, and spherical coordinates.

**Q4: **

Two points in a plane have polar coordinates and .

Determine the Cartesian coordinates of .

- A(2.115 m, 1.210 m)
- B(2.165 m, 1.250 m)
- C(2.225 m, 1.150 m)
- D(2.265 m, 1.130 m)
- E(2.100 m, 1.050 m)

Determine the Cartesian coordinates of .

- A( m, 3.095 m)
- B( m, 3.290 m)
- C( m, 3.140 m)
- D( m, 3.050 m)
- E( m, 3.000 m)

Determine the distance between the points, to the nearest centimeter.

**Q5: **

A circular polar orbit around Earth is an orbit that passes directly overhead at both the North Pole and the South Pole. A satellite in a circular polar orbit around Earth at an altitude of 400 km moves in its orbit form a point that is directly over the North Pole to a point that is at a latitude of . In determining the motion of the satellite, use a value of 6,371 km for the radius of Earth.

What is the magnitude of the displacement vector from to ?

At what angle below east is the direction of the displacement vector from to ?

**Q7: **

A student is trying to determine the acceleration of a feather as she drops it to the ground. If the student is looking to achieve a positive velocity and positive acceleration, what is the most sensible way to set up her coordinate system?

- AThe floor should be a coordinate of zero, and the upward direction should be considered positive.
- BHer hand should be a coordinate of zero, and the upward direction should be considered positive.
- CThe floor should be a coordinate of zero, and the downward direction should be considered negative.
- DHer hand should be a coordinate of zero, and the downward direction should be considered positive.