A person moves 30 𝑚 north and then20 𝑚 towards east and finally 30√2𝑚 insouth-west direction. The displacementof the person from the origin will be

To find the displacement of the person from the origin, we need to calculate the resultant of the three movements.

Step 1: Draw a diagram First, let's draw a diagram to visualize the movements. The person moves 30m north, then 20m east, and finally 30√2m in the south-west direction.

Step 2: Break down the movements into components Next, we break down each movement into its x (east-west) and y (north-south) components.

• The first movement is 30m north, which is 0m in the x direction and +30m in the y direction.
• The second movement is 20m east, which is +20m in the x direction and 0m in the y direction.
• The third movement is 30√2m in the south-west direction. This can be broken down into -30m in the x direction and -30m in the y direction (since south-west is a 45 degree angle, the x and y components are equal).

Step 3: Add up the components Now, we add up the x and y components separately:

• Total x component = 0m (from the first movement) + 20m (from the second movement) - 30m (from the third movement) = -10m
• Total y component = 30m (from the first movement) + 0m (from the second movement) - 30m (from the third movement) = 0m

Step 4: Calculate the displacement The displacement from the origin is the square root of the sum of the squares of the x and y components, which is √((-10m)^2 + (0m)^2) = 10m.

So, the displacement of the person from the origin is 10m.