Adding Vectors

1
Adding Vectors
E.g. A boat is pulled into harbour by two tug
boats at right angles as shown in the diagram
calculate its resultant speed
NOTE because they are vectors AND not in the
same direction we cant simply write down 5 ms-1
3 ms -1
Instead we make a triangle out of the two
velocities and use Pythagoras
2 ms -1
2
Triangle of forces
Make the two forces that we want to add together
into a triangle NOSE to TAIL. Like this
2 ms -1
3 ms -1
OR
3 ms -1
2 ms -1
Its a right angled triangle so use
Pythagoras Hypotenuse2 22 32
4 9
13 Result ? 13 3.6 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.
3
Subtracting Vectors
E.g. subtract Force B from Force A (which are at
right angles)
A
It is the same as adding but point the
subtracting force in the other direction
A
-B
B
Then nose to tail them, and do Pythagoras
4
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
300
Horizontal
250
2 ms -1
5
Occasionally you can resolve
10N
500
horizontal
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
500
Result 2 x 10 cos 50
10N
Note Pythagoras wont work in this case why
not?