– A man walks 50 meters due west, then 50 meters 60 north of west. Determine the magnitude and direction of the resultant displacement using the vector component method.

86.6, 45°

Explanation:

The diagram explains better.

Using vector component method:

We find the x and y components of the vectors :

For the first:

A = -50cos(0)i + 50sin(0)j

A = -50i

For the second:

B = -50cos(60)i + 50sin(60)j

B = -25i + 43.3j

The resultant vector is :

R = A + B

R = -50i - 25i + 43.3j

R = -75i + 43.3j

The magnitude is:

R = [(-75)² + (43.3)²]^½

R = 86.6m

The angle is

tanθ = (50/50) = 1

θ = 45°