Question

distance and displacement worksheet
name: adriana.p per3rd
for each question plot the path on the grid paper.

1. chanice drives her scooter 7 kilometres north. she stops for lunch and then drives 5 kilometres east. what distance did she cover? what was her displacement?
2. anthony walks to the pizza place for lunch. he walk 1 km east, then 1 km south and then 1 km east again. what distance did he cover? what was his displacement?
3. on his fishing trip justin rides in a boat 12 km south. the fish arent biting so they go 4 km west. they then follow a school of fish 1 km north. what distance did they cover? what was their displacement?
4. tara goes on a camel safari in africa. she travels 5 km north, then 3 km east and then 1 km north again. what distance did she cover? what was her displacement?
5. alex goes cruising on his dirt bike. he rides 700 m north, 300 m east, 400 m north, 600 m west, 1200 m south 300 m east and finally 100 m north. what distance did he cover? what was his displacement? (use 1cm = 100m)
6. jose buys a new moped. he travels 3 km south and then 4 km east. how far does he need to go to get back to where he started?

Explanation:

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Question 1

Step1: Calculate total distance

$7\ \text{km} + 5\ \text{km} = 12\ \text{km}$

Step2: Calculate displacement (Pythagoras)

$\sqrt{(7\ \text{km})^2 + (5\ \text{km})^2} = \sqrt{49 + 25} = \sqrt{74} \approx 8.60\ \text{km}$ (northeast direction)

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Question 2

Step1: Calculate total distance

$1\ \text{km} + 1\ \text{km} + 1\ \text{km} = 3\ \text{km}$

Step2: Net east/south distance

East: $1+1=2\ \text{km}$, South: $1\ \text{km}$

Step3: Calculate displacement

$\sqrt{(2\ \text{km})^2 + (1\ \text{km})^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.24\ \text{km}$ (southeast direction)

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Question 3

Step1: Calculate total distance

$12\ \text{km} + 4\ \text{km} + 1\ \text{km} = 17\ \text{km}$

Step2: Net south/west distance

South: $12-1=11\ \text{km}$, West: $4\ \text{km}$

Step3: Calculate displacement

$\sqrt{(11\ \text{km})^2 + (4\ \text{km})^2} = \sqrt{121 + 16} = \sqrt{137} \approx 11.70\ \text{km}$ (southwest direction)

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Question 4

Step1: Calculate total distance

$5\ \text{km} + 3\ \text{km} + 1\ \text{km} = 9\ \text{km}$

Step2: Net north/east distance

North: $5+1=6\ \text{km}$, East: $3\ \text{km}$

Step3: Calculate displacement

$\sqrt{(6\ \text{km})^2 + (3\ \text{km})^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.71\ \text{km}$ (northeast direction)

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Question 5

Step1: Calculate total distance

$700+300+400+600+1200+300+100 = 3600\ \text{m} = 3.6\ \text{km}$

Step2: Net north/south distance

North: $700+400+100=1200\ \text{m}$, South: $1200\ \text{m}$, Net north-south: $1200-1200=0\ \text{m}$

Step3: Net east/west distance

East: $300+300=600\ \text{m}$, West: $600\ \text{m}$, Net east-west: $600-600=0\ \text{m}$

Step4: Calculate displacement

$\sqrt{(0)^2 + (0)^2} = 0\ \text{m}$

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Question 6

Step1: Calculate return distance (displacement)

$\sqrt{(3\ \text{km})^2 + (4\ \text{km})^2} = \sqrt{9 + 16} = \sqrt{25} = 5\ \text{km}$ (northwest direction)

Answer:

1. Distance: $12\ \text{km}$; Displacement: $\approx 8.60\ \text{km}$ northeast
2. Distance: $3\ \text{km}$; Displacement: $\approx 2.24\ \text{km}$ southeast
3. Distance: $17\ \text{km}$; Displacement: $\approx 11.70\ \text{km}$ southwest
4. Distance: $9\ \text{km}$; Displacement: $\approx 6.71\ \text{km}$ northeast
5. Distance: $3600\ \text{m}$; Displacement: $0\ \text{m}$
6. $5\ \text{km}$ northwest