a person move 30 m north then 20 m east then 30root2 m south west .find displacement

To find the displacement of a person who moves in different directions, we can break down the movements into components and then use the Pythagorean theorem to calculate the overall displacement. Let's analyze the movements step by step.

Movement Breakdown

The person makes three distinct movements:

• 30 meters north
• 20 meters east
• 30√2 meters southwest

Understanding Directions

Before we calculate the displacement, it's important to clarify the direction of the last movement. Moving southwest means the person is moving at a 45-degree angle towards the south and west. This can be broken down into its components:

• Southwest movement can be split into south and west components.
• Since the angle is 45 degrees, both components will be equal.

Calculating Components of the Southwest Movement

For the southwest movement of 30√2 meters:

• South component = (30√2) * cos(45°) = 30 meters
• West component = (30√2) * sin(45°) = 30 meters

Net Displacement Calculation

Now, let's summarize the total movements in the north-south and east-west directions:

North-South Direction

• North: 30 meters
• South: 30 meters

The net movement in the north-south direction is:

30 m (north) - 30 m (south) = 0 m

East-West Direction

• East: 20 meters
• West: 30 meters

The net movement in the east-west direction is:

20 m (east) - 30 m (west) = -10 m (which means 10 meters west)

Final Displacement Calculation

Now we have the net movements:

• North-South: 0 meters
• East-West: 10 meters west

Since there is no movement in the north-south direction, the displacement is purely in the east-west direction. To find the total displacement, we can use the Pythagorean theorem, but in this case, it simplifies to just the distance in the east-west direction:

Displacement = 10 meters west

Conclusion

In summary, after moving 30 meters north, 20 meters east, and then 30√2 meters southwest, the person's overall displacement is 10 meters to the west. This example illustrates how to break down movements into components and calculate net displacement effectively.