Question

Hello :) how to do 25 (b) ?

Answer 1

Step-by-step explanation:

You first solve point a by finding the components
`< R_x; R_y >` of the resulting vector, which will be

`< 0 + 40 * cos 30\° + 30 * cos (- 50\°); 20 + 40 * sin 30\° + 30 * sin (-50\°) >`

Notice that since the 50° angle is taken clockwise, we consider it negative, while the 30° is considered positive.

Plugging the values in a calculator or a spreadsheet (if you are using excel or similar programs, don't forget to convert the angle in radians!) you will get the components, namely
`< 53.92;17.02 >`

At this point magnitude is defined as
`R = √(R_x^2 + R_y^2)` while for direction you first take the ratio
`R_y/R_x` and again, with a calculator, you get the inverse tangent of it. The result will be a number between
`-\frac{\pi}2` and
`\frac\pi2` (-90° and 90°) which tells you the angle the line containing your vector forms with the positive x axis, in our case it's
`tan^-^1 (53.92/17.02) \approx 17.52` (ie, it sits on the red line)

At this point, based on the fact that both are positive, the end point of the vector is in the first quadrant.