If = [10 m, 30°] and = [25 m, 130°], what is the direction of the sum of these two vectors?
A) 17°
B) 73°
C) 107°
D) 163°
E) 100°

Question

If  = [10 m, 30°] and  = [25 m, 130°], what is the direction of the sum of these two vectors?
A) 17° 
B) 73° 
C) 107° 
D) 163° 
E) 100°

Quizplus · Accepted Answer

Using trigonometry and vector addition, we can find the x and y components of each vector:
11eb6adc_eda3_6594_b0cf_7b5f3de15b28_TB8245_11: x = 10 * cos(30°) = 8.66 m, y = 10 * sin(30°) = 5 m 
11eb6adc_eda3_8ca5_b0cf_43bdbeda4880_TB8245_11: x = 25 * cos(130°) = -18.78 m, y = 25 * sin(130°) = 16.06 m

To find the x and y components of the sum vector, we can simply add the x components together and the y components together:
x = 8.66 - 18.78 = -10.12 m 
y = 5 + 16.06 = 21.06 m

Using these components, we can find the magnitude and direction of the sum vector:
magnitude = sqrt((-10.12)^2 + (21.06)^2) = 23.43 m 
direction = tan^-1(21.06 / -10.12) = 107.41°

Therefore, the direction of the sum vector is 107°.

If = [10 M, 30°] and = [25