Question

The displacement vector from your house to the library is 520 m long, pointing 40 ∘ north of east.What are the x-component (x-axis is directed from west to east) of this displacement vector?What are the y-component (y-axis is directed from south to north) of this displacement vector?

Answer 1

Answer:

398.3 m, 334.2 m

Explanation:

The magnitude of the displacement vector is

v = 520 m

And its direction is

$\theta=40^{\circ}$

measured as north of east.

The x-component of this vector is given by:

$v_x = v_0 cos \theta = (520)cos 40^{\circ}=398.3 m$

While the y-component is given by

$v_y = v_0 sin \theta =(520)sin 40^{\circ}=334.2 m$