<h2>
1. Magnitude 3.5 m/s, direction angle 35°, magnitude 4 m/s, direction angle 150°.</h2><h3>
Matches to 4.05 m/s</h3>
First of all, let's write this statement in vector form. For the fist vector we have:
<u>Magnitude 3.5 m/s, direction angle 35°:</u>
Let's say this is vector , so the magnitude is:
And the direction is defined as:
So the components are:
So vector is:
For the second vector:
<u>Magnitude 4 m/s, direction angle 150°:</u>
Let's say this is vector , so the magnitude is:
And the direction is defined as:
So the components are:
So vector is:
THE SUM OF THESE TWO VECTORS IS:
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
<h2>
2. Magnitude 4.5 m/s, direction angle 55°, magnitude 3 m/s, direction angle 135°.</h2><h3>
Matches to 5.83 m/s</h3>
<u>Magnitude 4.5 m/s, direction angle 55°:</u>
Let's say this is vector , so the magnitude is:
And the direction is defined as:
So the components are:
So vector is:
For the second vector:
<u>Magnitude 3 m/s, direction angle 135°:</u>
Let's say this is vector , so the magnitude is:
And the direction is defined as:
So the components are:
So vector is:
THE SUM OF THESE TWO VECTORS IS:
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
<h2>
3. Magnitude 3 m/s, direction angle 70°, magnitude 3 m/s, direction angle 135°.</h2><h3>
Matches to 3.32 m/s</h3>
<u>Magnitude 4.5 m/s, direction angle 55°:</u>
This is vector , so the magnitude is:
Direction:
Components:
So:
For the second vector:
<u>Magnitude 5 m/s, direction angle 210°:</u>
:
Direction:
Components:
Then:
THE SUM OF THESE TWO VECTORS IS:
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
<h2>
4. Magnitude 6 m/s, direction angle 120°, magnitude 2 m/s, direction angle 140°.</h2><h3>
Matches to 5.29 m/s</h3>
<u>Magnitude 6 m/s, direction angle 120°:</u>
Direction:
Components:
So:
For the second vector:
<u>Magnitude 2 m/s, direction angle 240°:</u>
:
Direction:
Components:
Then:
THE SUM OF THESE TWO VECTORS IS:
THE MAGNITUDE OF THE RESULTANT VECTOR IS: