Question

Vector A has a magnitude of 4.00 m and points 75.0° above the +x axis, vector B has a magnitude of 7.90 m and points 20.0° below the -x axis. Find the direction of R where R = A+B.

O 30.0° above the -x axis
O 10.3° above the -x axis
O 16.0° above the -x axis
O 16.0° above the +x axis
O 10.3° above the +x axis

Answer 1

The direction of the resultant vector is 10.3⁰ below - x axis. (Option B).

How to calculate the direction of the resultant vector?

The direction of the resultant vector is calculated by applying the following formula as shown below.

The sum of the vectors in x - direction

Rx = Ax + Bx

Rx = 4m cos(75) - 7.9 cos(20)

Rx = -6.388 m

The sum of the vectors in y - direction

Ry = Ay + By

Ry = 4m sin(75) - 7.9 sin(20)

Ry = 1.16 m

The direction of the resultant vector is calculated as;

tan θ = Ry/Rx

tan θ = 1.16 / -6.388

tan θ = - 0.1816

θ = arc tan (-0.1816)

θ = -10.3⁰

Thus, the direction of the resultant vector is 10.3⁰ below - x axis.