Physics Question?The rectangle shown in Figure P3.57 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 24.0°.

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1 Answer
Feb 5, 2018

Perimeter = 2 = 14.62
C = 13.4
phi = 34.9

Explanation:

Whether using vectors or diagrams, it is essentially a geometry problem. The two trianglyes defined by the angles and the given sides (vectors) with the x-axis can be solved for the rectangle side lengths.

The "A" triangle has a hypotenuse of 10 and an angle of 50, from which we calculate x_1/10 = cos(50) and y_1/10 = sin(50)

The "B" triangle has a hypotenuse of 12 and an angle of 24, from which we calculate x_2/12 = cos(24) and y_2/12 = sin(24)_2

The sides are then x_1 - x_2 and y_1 - y_2.

x_1 = 6.43 ; y_1 = 7.66
x_2 = 10.96 ; y_2 = 4.88

x_1 - x_2 = 4.53 and y_1 - y_2 = 02.78.
Perimeter = 2xx(4.53 + 2.78) = 14.62

To find the length and angle of the vector to the far corner we construct another triangle with Hypotenuse C, height y_1 and base of x_2.
C^2 = x_2^2 + y_1^2 ; C^2 = 120.1 + 58.7
C = 13.4
The angle is thus tan(phi) = y_1/x_2 = 7.66/10.96 = 0.7
phi = 34.9