Adding VectorsE.g. A boat is pulled into harbour by two tug boats at right angles as shown in the diagram – calculate its resultant speed

3 ms -1

2 ms -1

NOTE – because they are vectors AND not in the same direction we

can’t simply write down 5 ms-1

Instead we make a triangle out of the two

velocities and use Pythagoras

Triangle of forces

3 ms -1

Make the two forces that we want to add together into a triangle NOSE to TAIL. Like this …

2 ms -1

The result of adding these two vectors is the missing

side of the triangle.

Its length will be the speed of the ship and its direction

will be as drawn.

It’s a right angled triangle so use Pythagoras:

Hypotenuse2 = 22 + 32

= 4 + 9

= 13

Result = 13 = 3.6 ms-1

2 ms -13 ms -1

OR

Subtracting VectorsE.g. subtract Force B from Force A (which are at right

angles) …

A

B

It is the same as adding – but point

the subtracting force in the other

direction-B

Then nose to tail them, and do Pythagoras

A

Vectors that are not at right angles

Draw a scale drawing and then a parallelogram around the two forces – the resultant is the diagonal:

3 ms -1

2 ms -1

Horizontal 300

250

Occasionally you can resolve

horizontal500

500 Special case:

The forces are equal and at the same angle – therefore the resultant will be horizontal – therefore resolve both forces

to the horizontal and add them

Result = 2 x 10 cos 50

10N

10N

Note – Pythagoras won’t work in this case – why not?