Find the resultant vector of two vectors that have a direction of 48° and magnitudes of 6 and 2, respectively.
A)magnitude of 8 with direction of 0°
B)magnitude of 4 with direction of 48°
C)magnitude of 8 with direction of 48°
D)magnitude of 16 with direction of 48°

Question

Quizplus · Accepted Answer

To find the resultant vector, we need to use the formula:

resultant = (vector 1 + vector 2)

We can break down each vector into its x and y components using trigonometry:

Vector 1: magnitude = 6, direction = 48°
x component = 6 cos 48° = 3.89
y component = 6 sin 48° = 4.58

Vector 2: magnitude = 2, direction = 48°
x component = 2 cos 48° = 1.56
y component = 2 sin 48° = 1.83

Adding the x and y components, we get:

x component of resultant = 3.89 + 1.56 = 5.45
y component of resultant = 4.58 + 1.83 = 6.41

Using the Pythagorean theorem, we can find the magnitude of the resultant vector:

magnitude of resultant = sqrt((5.45)^2 + (6.41)^2) = 8.35

We can also use trigonometry to find the direction of the resultant vector:

tan(theta) = (y component of resultant)/(x component of resultant)
theta = arctan(6.41/5.45) = 48.02°

Therefore, the correct answer is C: magnitude of 8 with direction of 48°.

Find the Resultant Vector of Two Vectors That Have a Direction