Question
Asked Sep 1, 2019
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Referring to the vectors in the figure, express the sum A⃗ +B⃗ +C⃗  in unit vector notation.
(Figure 1)
Express your answer using two significant figures.
Enter the x and y components of the vector separated by comma
y
1.0 m
A
25°
1.5 m
40°
19°
2.0 m
B
D
1.5 m
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y 1.0 m A 25° 1.5 m 40° 19° 2.0 m B D 1.5 m

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Expert Answer

Step 1

The x-component of the vector sum is given by

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(1) R ABC Here, R is the x-component of the sum A+ B+č , A, is the x-component of A , B is the x- component of B and C is the x-component of C The expression for the x-component of a vector P is given by P Pcos e Here, P is the magnitude of Pand 0 is the angle the vector makes with the positive x-axis The magnitude of the vector A is 1.5m. The angle it makes with the positive x-axis is 40° .The value of A, is given by 4 (1.5 m) cos 40° The magnitude of the vector Bis 2.0m. The angle it makes with the positive x-axis is -19° (negative since the angle is taken clockwise) .The value of B, is given by B (2.0 m) cos(19°) The magnitude ofthe vector C is 1.0m. The angle it makes with the positive x-axis is 180°-25° =155° .The value of C is given by c (1.0 m)cos (155°)

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Step 2

Put the above three equations in equation (1).

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R (1.5 m cos 40°+ (2.0 m)cos (-190)+(1.0 m) cos (155°) == = 2.1 m The y-component of the vector sum is given by R A,BC Here, R is the y-component of the sum A+ B+c , A, is the y-component of A , B is the y- component of B and C is the y-component of C (2) = The expression for the y-component of a vector P is given by P Psin e The value of A, is given by A (1.5 m)sin 400 The value of B is given by B, (2.0 m) sin (190) The value of C, is given by c, (1.0 m)sin (155°)

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Step 3

Put the above three equatio...

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R, (1.5 msin 40°+(2.0 m)sin (-19°)+(1.0 m)sin (155°) = 0.74 m The x and the y components of the vector sum AB+C is given by (2.1 m, 0.74 m)

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