Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the resultant electric field when there are two fields, E1 and E2, where E1 is directed vertically upward and has magnitude 96 V/m and E2 is directed 48° to the left of E1 and has magnitude 165 V/m.

(a) Find the speed of a satellite moving around the earth in a circular orbit that has a radius equal to six times the earth's radius of 6.38 106 m.

(b) Find the satellite's orbital period.

To find the resultant electric field, we can use vector addition.

1. Convert the given magnitudes and directions into Cartesian coordinates:
- E1 (vertical upward) has a magnitude of 96 V/m and can be written as E1 = 96i, where i is the unit vector in the upward direction.
- E2 (48° to the left of E1) has a magnitude of 165 V/m. To convert the direction into Cartesian coordinates, we can decompose it into its horizontal (x) and vertical (y) components. The x-component is 165 * cos(48°), and the y-component is 165 * sin(48°).

2. Perform vector addition:
- Add the two vectors component-wise. The x-components of E1 and E2 will add up together, and the same goes for the y-components.
- For the x-component, we have: Ex = 96 + 165 * cos(48°).
- For the y-component, we have: Ey = 165 * sin(48°).

3. Calculate the magnitude and direction of the resultant vector:
- The magnitude of the resultant electric field is given by the Pythagorean theorem: |E| = √(Ex² + Ey²).
- The direction can be found using trigonometric functions: angle = tan⁻¹(Ey / Ex).

Plug the values into the equations to get the final result.