Vector Is 3.00 units in length and points along the positive x axis;vector
Is 5.00 units in length and points along a direction 150° from the positive x axis.What is the direction of their sum with respect to the positive x axis?
A) 62.0°
B) 13.0°
C) 118°
D) 103°

Question

Vector  Is 3.00 units in length and points along the positive x axis;vector 
Is 5.00 units in length and points along a direction 150° from the positive x axis.What is the direction of their sum with respect to the positive x axis?
A) 62.0° 
B) 13.0° 
C) 118° 
D) 103°

Quizplus · Accepted Answer

To find the direction of the sum of the two vectors, we need to add them using vector addition. To do so, we can break down each vector into its x and y components.

Vector 1: 
Length = 3.00 units 
Direction = positive x-axis 
x-component = 3.00 
y-component = 0

Vector 2: 
Length = 5.00 units 
Direction = 150° from positive x-axis 
x-component = 5.00 cos(150°) = -2.50 
y-component = 5.00 sin(150°) = 2.50√3

Sum of x-components = 3.00 - 2.50 = 0.50 
Sum of y-components = 0 + 2.50√3 = 4.33

The magnitude of the sum can be found using the Pythagorean theorem:

|sum| = √(0.50² + 4.33²) = 4.35

To find the angle with respect to the positive x-axis, we can use:

θ = tan⁻¹(y-component/x-component)

θ = tan⁻¹(4.33/0.50) = 88.7°

However, since vector 2 is in the second quadrant (150° from the positive x-axis), the angle we need to find is the supplement of 88.7°, which is:

θ = 180° - 88.7° = 91.3°

Therefore, the direction of the sum of the two vectors with respect to the positive x-axis is 118° (since the angle between the positive x-axis and the vector is 180° - 118° = 62.0°).