A car travels 15km northwards. 5km eastwards, 10km southwards, and 5km westwards to arrive at point P. Find its total displacement
D = 15i + 5 -10i - 5 = 5i = 5 km Northwards.
To find the total displacement of the car, we need to determine the straight-line distance and direction from the starting point to the ending point.
1. Start by drawing a diagram to visualize the car's movement.
- Mark the starting point and label it as S.
- Mark the ending point and label it as P.
- Draw arrows representing the distances traveled in each direction.
2. Break down the given distances into their respective components (north, south, east, and west).
- The car travels 15km northwards, so the north component is 15km.
- The car travels 5km eastwards, so the east component is 5km.
- The car travels 10km southwards, so the south component is 10km.
- The car travels 5km westwards, so the west component is 5km.
3. Add up the north and south components to get the net north component.
- Net north component = North component - South component
= 15km - 10km
= 5km north
4. Add up the east and west components to get the net east component.
- Net east component = East component - West component
= 5km - 5km
= 0km
5. Calculate the total displacement using the Pythagorean theorem.
- Total displacement = √(Net north component^2 + Net east component^2)
= √(5km^2 + 0km^2)
= √(25km^2)
= 5km
Therefore, the car's total displacement is 5km, in the north direction.