1. The document describes different methods for calculating resultant vectors from component vectors including addition, subtraction, parallelogram, and polygon methods.
2. Examples are provided for calculating distances and directions traveled when combining movements in the same and opposite directions as well as at angles to each other.
3. Practice exercises are included at the end to calculate resultant displacements from given component distances and directions of travel.
3. SAME DIRECTION
Addition
1. Chacha walks 300m East, stops to rest and then
continues 400 m East.
𝑑1 = 300 𝑚 𝐸 𝑑2 = 400 𝑚 𝐸
Adding the two vectors we have 300mE + 400 m E =
700 m E
𝒅 𝒓 = 𝟕𝟎𝟎 𝐦 𝐄
4. Subtraction
2. Mimi walks home from school 300 m East and remembers
that she has to bring home her Science book which a
classmate borrowed. She walks back 500 m West to her
classmate’s house.
OPPOSITE DIRECTION
𝑑1 = 300 𝑚 𝐸
𝑑2 = 500 𝑚 𝑊
Since it has two dimensions, the vectors will be subtracted. Answer: 500 m W –
300 m E = 200m W
𝒅 𝒓 = 𝟐𝟎𝟎 𝐦 𝐖
5. PARALLELOGRAM METHOD
3. Kate walks 500 m East and then turns to North
and walks 300 m.
𝟑𝟏 𝟎
𝑑1 = 500 𝑚 𝐸
𝑑2 = 300 𝑚 𝑁
6. POLYGON METHOD
4. Gino walks 600m East, then turns 400 m North and finally
walks 300 m West.
𝟓𝟒 𝟎
𝑑2 = 400 𝑚 𝑁
𝑑3 = 300 𝑚 𝑊
𝑑1 = 600 𝑚 𝐸
7. PRACTICE
EXERCISE
1. Tracy walks from her home 100 ft West and then when
she reached the store, she noticed that her wallet was
lost. She walked back to the East and then find her
wallet on the road at exactly 50 ft away from the store.
Find the resultant vector.
2. A car moves 100 km North, then turns 200 km West.
What is the total displacement of the car?
3. A hiker walks 50 m East, then 200m South and finally,
400 m West. What is the resultant displacement of the
hiker from the starting point?
SCALE: 1cm = 50 units
