Question

I need help in my physics class and show me how it’s done

Answer 1

If we have the angle and magnitude of a vector A we can find its Cartesian components using the following formula

`A_x = |A|cos(\alpha)\\\\A_y = |A|sin(\alpha)`

Where | A | is the magnitude of the vector and
`\alpha` is the angle that it forms with the x axis in the opposite direction to the hands of the clock.

In this problem we know the value of Ax and Ay and we need the angle
`\alpha`.

Vector A is in the 4th quadrant

So:

`A_x = 6\\\\A_y = -6.5`

So:

`|A| = √(6^2 + (-6.5)^2)\\\\|A| = 8.846`

So:

`Ay = -6.5 = 8.846cos(\alpha)\\\\sin(\alpha) = (-6.5)/(8.846)\\\\sin(\alpha) = -0.7348\\\\\alpha = sin^(- 1)(- 0.7348)`

`\alpha` = -47.28 ° +360° = 313 °

`\alpha` = 313 °

Option 4.