Question

Hello :) how to do 25 (b) ?

Answer 1

Answer:

Explanation:

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

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

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 $R = \sqrt{R_x^2 + R_y^2}$ 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.