Question

Each of the following vectors is given in terms of its x- and y-components.

Part A

vx = 23 m/s , vy = 45 m/s . Find the vector's magnitude.

Part B

vx = 23 m/s , vy = 45 m/s . Find the vector's direction.

Part C

ax = 9.0 m/s2 , ay = -3.5 m/s2 . Find the vector's magnitude.

Part D

ax = 9.0 m/s2 , ay = -3.5 m/s2 . Find the vector's direction

Answer 1

Concepts and reason

The problem deals with the concept of the vector’s magnitude and the direction of the vector. As if the magnitude and direction of the other vectors are known then the magnitude and direction of the resultant vector can be determined.

First determine the magnitude of the resultant velocity vector then determine the direction of the velocity.

Fundamentals

The magnitude of the vector is the length of the vector.

For a two dimensional vector the formula of the magnitude of the vector is as:

Here and are the magnitude of two vectors.

And the direction of the vector is as:

(A)

The resultant velocity vector will be when the magnitude of velocity components are known:

Substitute the magnitude of velocity vector in the directionand velocity vector in the direction

(B)

The direction of the vector is as:

Substitute the magnitude of velocity vector in the directionand velocity vector in the direction

(C)

The acceleration vector is the direction is as:

The acceleration vector is the direction is as:

The resultant acceleration vector will be:

Substitute the magnitude of acceleration vector in the directionand acceleration vector in the direction as:

(D)

The direction of the acceleration vector is as:

Substitute the magnitude of acceleration vector in the directionand acceleration vector in the direction as:

Therefore the negative sign implies that the direction of the acceleration vector is clockwise from x-axis at an angle of.

Ans: Part A

The magnitude of the resultant velocity vector will be.

Part C

The magnitude of the resultant acceleration vector will be.