A person walks 25 m west and then 45 m at the angle of 60 degrees north of east what is the magnitude of the total displacement?

To solve this question, we need to use the component method and split our displacements into their x and y vectors. We will assign north and east as the positive directions.

The first movement of 25m west is already split. x = - 25m, y = 0m.

The second movement of 45m [E60N] needs to be split using trig.

x = 45cos60 = 22.5m

y = 45sin60 = 39.0m

Then, we add the two x and two y displacements to get the total displacement in each direction.

x = - 25m + 22.5m = - 2.5m

y = 0m + 39.0m

We can use Pythagorean theorem to find the total displacement.

d² = x² + y²

d = √ (-2.5² + 39²)

d = 39.08m

And then we can use tan to find the angle.

inversetan (y/x) = angle

inversetan (39/2.5) = 86.3

Therefore, the total displacement is 39.08m [W86.3N]