Question

Help PLease

Answer 1

Answer:

1. The horizontal component is 37.74 N due to east

The vertical component is 16.02 N due to north

2. The magnitude of the resultant vector is 11.6338 m

Explanation:

The resultant vector is the vector sum of two or more vectors

It has magnitude and direction

Its magnitude = $\sqrt{x^{2}+y^{2}}$, where x is its component

in the direction of x-axis and y is its component in the direction of y-axis

Its direction = $tan^{-1}\frac{y}{x}$ with respect to x-axis

So the components of the resultant vector of magnitude R and direction

Ф with the positive part of x-axis are:

Horizontal component = R cosФ

Vertical component = R sinФ

1.

Slanted vector has a magnitude of 41 N and is at an angle of 23°

north of east

We need to find the horizontal and vertical components with their

directions

North of east means 23° between east and the ray of the vector

If we consider that east is the positive part of the x-axis

Then R = 41 N and Ф = 23°

The horizontal component = (41) cos(23) = 37.74 N due to east

The vertical component = (41) sin(23) = 16.02 N due to north

The horizontal component is 37.74 N due to east

The vertical component is 16.02 N due to north

2.

A horizontal component vector has a magnitude of 11 m

If the resultant vector forms an angle with this component of 19°

The horizontal component = R cosФ

11 = R cos(19)

Divide both sides by cos(19)

11.63 = R

The magnitude of the resultant vector is 11.6338 m