Question

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?

Answer 1

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]