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
ϕ=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 x110=cos(50) and y110=sin(50)

The "B" triangle has a hypotenuse of 12 and an angle of 24, from which we calculate x212=cos(24) and y212=sin(24)_2

The sides are then x1x2 and y1y2.

x1=6.43 ; y1=7.66
x2=10.96 ; y2=4.88

x1x2=4.53 and y1y2=02.78.
Perimeter = 2×(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 y1 and base of x2.
C2=x22+y21 ; C2=120.1+58.7
C=13.4
The angle is thus tan(ϕ)=y1x2=7.6610.96=0.7
ϕ=34.9