Answer to Question #244560 in Physics for Asmar

Question #244560

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.


1
Expert's answer
2021-10-03T13:25:02-0400

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


"A_x=10\\cos50\u00b0,\\\\\nA_y=10\\sin50\u00b0.\\\\\nB_x=12\\cos30\u00b0,\\\\\nB_y=12\\sin30\u00b0.\\\\\\space\\\\\na=B_x-A_x,\\\\\nb=A_y-B_y.\\\\\np=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 Ay so, having x-coordinate equal to Bx, the magnitude of R:


"R=\\sqrt{B_x^2+A_y^2}=12.9\\text{ m},\\\\\\theta=\\arctan\\frac{A_y}{B_x}=36\u00b0.\\\\\\space\\\\\n\\vec R=12.9\\angle36\u00b0."


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