A car travels 5km to east. Then it goes 3km to north and then 2km to west. What is the displacement the car has traveled?

end position: 3E,3N

displacement: 3√2 NE

a man drove his car north west for a distance of 10km then east for 40km and then south for 60km calculate the overall displacement and direction of the car from the starting point

To find the displacement of the car, we need to calculate the net distance and direction from the starting point to the final point.

Step 1: Draw a diagram to represent the car's movements.

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.
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S(start) ———> 5km E ———> 3km N ———> 2km W
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V(final)

Step 2: Identify the vertical and horizontal components of the car's movement.

Vertical component: The car traveled 3km north.
Horizontal component: The car traveled 5km east and 2km west, which cancels each other out.

Step 3: Calculate the net displacement.

Vertical displacement: 3km north
Horizontal displacement: 5km east - 2km west = 3km east

Step 4: Apply the Pythagorean theorem to find the magnitude of the displacement.

Displacement = √(vertical displacement^2 + horizontal displacement^2)
= √(3^2 + 3^2)
= √(9 + 9)
= √18
= 3√2

Therefore, the displacement of the car is 3√2 km.

To find the displacement of the car, we need to calculate the net distance between the starting point and the ending point. Displacement considers both the distance traveled and the direction.

In this case, the car starts by traveling 5km to the east. This means it is 5km to the right of the starting point.

Next, the car goes 3km to the north. This means it is 3km above the previous position.

Lastly, the car travels 2km to the west. This means it is 2km left of the previous position.

To calculate the net displacement, we need to add up the horizontal distances (east and west) separately from the vertical distances (north and south).

Horizontal displacement = distance traveled to the east - distance traveled to the west
Vertical displacement = distance traveled to the north - distance traveled to the south

In this case:
Horizontal displacement = 5km (east) - 2km (west) = 3km to the east
Vertical displacement = 3km (north) - 0km (south) = 3km to the north

Now, we can calculate the net displacement using the Pythagorean theorem:

Net displacement = √(Horizontal displacement^2 + Vertical displacement^2)
= √(3^2 + 3^2)
= √(9 + 9)
= √18
≈ 4.24 km

Therefore, the displacement of the car is approximately 4.24 km.