A man walks 30 m towards north then 20 m towards east and last 30√2 m towards South West .The displacement from origin is.?

Question

Answer

Answer

Answer

Approx. 6.371

Answer

Given information:
- The man walks 30 m towards the north.
- Then, he walks 20 m towards the east.
- Finally, he walks 30√2 m towards the South West.

Analysis:
To find the displacement from the origin, we need to calculate the net distance and direction travelled by the man.

Calculations:
We can break down the given information into its components to simplify the calculations.

Step 1: Walking towards the north
- The man walks 30 m towards the north.
- This means he moves in the positive y-direction by 30 m.

Step 2: Walking towards the east
- The man walks 20 m towards the east.
- This means he moves in the positive x-direction by 20 m.

Step 3: Walking towards the South West
- The man walks 30√2 m towards the South West.
- This means he moves in the negative y-direction and negative x-direction simultaneously.
- The displacement in the y-direction is -30√2 m.
- The displacement in the x-direction is -30√2 m.

Net Distance:
To calculate the net distance, we need to find the magnitude of the displacement in both the x and y directions.

- Displacement in y-direction: -30√2 m
- Displacement in x-direction: -30√2 m

Using the Pythagorean theorem, we can calculate the net distance:

Net distance = √((-30√2)^2 + (-30√2)^2)
= √(900*2 + 900*2)
= √(1800 + 1800)
= √3600
= 60 m

Direction:
To find the direction of the displacement, we can use the tangent function:

Direction = tan^(-1)((-30√2)/(-30√2))
= tan^(-1)(1)
= 45°

Final Answer:
The displacement from the origin is 60 m in the direction of 45°.

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