Question

The displacement vector from your house to the library is 740 m long, pointing 40 ∘ north of east. Part A What are the x-component (x-axis is directed from west to east) of this displacement vector?

Answer 1

The horizontal component of the displacement is 566.9 m

Explanation:

The horizontal (x-) and vertical (y-) components of a vector on the Cartesian plane can be found as follows:

$v_x = v cos \theta$

$v_y = v sin \theta$

where

v is the magnitude of the vector

$\theta$ is the angle representing the direction of the vector, measured as above the x-axis.

In this problem, we have:

v = 740 m (magnitude of the vector)

$\theta=40^{\circ}$ (direction of the vector)

Therefore, the two components are

$v_x = (740)(cos 40)=566.9 m$

$v_y = (740)(sin 40)=475.7 m$

Learn more about vector components:

brainly.com/question/2678571

#LearnwithBrainly