Question

The rectangle shown in a Figure has sides parallel to the x and y axes. The position vectors of two

corners are A = 10.0 m at 50.0° and B = 12.0 m at 30.0°. (a) Find the perimeter of the rectangle. (b) Find the magnitude

and direction of the vector from the origin to the upper right corner of the rectangle.

Answer 1

Find the x- and y-projection of A and B:

$$A_x=10\cos50°,\\ A_y=10\sin50°.\\ B_x=12\cos30°,\\ B_y=12\sin30°.\\\space\\ a=B_x-A_x,\\ b=A_y-B_y.\\ p=2(a+b)=2(B_x-A_x+A_y-B_y)=11.2\text{ m}.$$

The y-coordinate of the top right corner is A_y so, having x-coordinate equal to B_x, the magnitude of R:

$$R=\sqrt{B_x^2+A_y^2}=12.9\text{ m},\\\theta=\arctan\frac{A_y}{B_x}=36°.\\\space\\ \vec R=12.9\angle36°.$$