This is the worksheet for a simple math and physics tutorial aimed at middle to high schoolers (grades 9 and 10), explaining how to add simple vectors. What do we mean by simple vectors? Any two vectors that are both horizontal, or both vertical. The associated video (http://youtu.be/FzRpwgWUeIE) goes through conventions for attributing positive and negative signs to vectors, as well as three examples. This worksheet goes through five exercises, with worked through answers that are colourful and engaging for anyone.

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How to add SIMPLE vectors
The video associated with this worksheet (http://youtu.be/OOBm8ag1ZM0) reviews how to add simple
vectors. What do we mean by simple vectors? Any two vectors that are both horizontal, or both vertical
(like the two examples below).
There'll be another video out shortly on how to add different vectors together (we will update this
worksheet when it's available - alternatively subscribe to our YouTube channel to keep up to date).
The video goes through conventions for attributing positive and negative signs to vectors, as well as
three examples. Please make sure to check it out so you know what to do to answer the exercises on the
following pages.

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Exercise 1.
The below two boats are each travelling to the east. The pink boat is travelling at a velocity of 2 m/s,
whereas the red one is travelling at a velocity of 1.5 m/s. If a wind current started flowing in a easterly
direction at a velocity of 3 m/s, what would be their respective velocities?
Exercise 2.
A force of 50 N is exerted on the car below, to the left. If the force of friction (to the right) is 20 N,
what is the resultant force?
Exercise 3.
The aeroplane below is travelling at a velocity of 600 miles per hour to the east, when it experiences a
headwind of 20 miles per hour to the west. What is the resultant velocity of the plane?

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Exercise 4.
There are three forces acting on the below object. What is the net force?
Exercise 5.
There are three forces acting on the below object. What is the net force?

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Answers
Exercise 1.
You don't need to draw anything elaborate, but it helps to always draw the vectors, to make sure you
get them in the right direction.
The pink boat's resultant velocity = +2 m/s + +3 m/s
= +5m/s (or 5 m/s to the east)
The red boat's resultant velocity = +1.5 m/s + +3 m/s
= +4.5 m/s (or 4.5 m/s to the east)
Exercise 2.
The resultant force on the car is = +20 N + -50 N
= -30N (or 30 N to the west)

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Exercise 3.
The resultant velocity = +600 mi/hr + -20 mi/hr
= +580 mi/hr (or 580 mi/hr to the east)
Exercise 4.
The resultant force = -5N + - 10N + +2N
= -13N (or 13 N to the left or west)

6. Exercise 5.
The resultant force = -1N + +2N + +6N
= +7N (or 7N upwards / to the north)
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