A man goes 10m towards North, then 20m towards east then displacement is

The correct option is 22.5m.

To find the displacement, we need to determine the shortest straight-line distance between the man's initial starting position and his final position.

Step 1: Understand the directions
The man first travels 10 meters towards the North, and then turns and travels 20 meters towards the East. Since North and East directions are perpendicular to each other (at an angle of 90°), this motion forms a right-angled triangle where:
- The vertical leg (Northward journey) is 10 m.
- The horizontal leg (Eastward journey) is 20 m.
- The hypotenuse represents the straight-line displacement vector.

Step 2: Apply the Pythagorean Theorem
According to the Pythagorean theorem, the hypotenuse (displacement) can be calculated using the formula:

$\text{Displacement}=\sqrt{{\left(\text{Northward Distance}\right)}^2+{\left(\text{Eastward Distance}\right)}^2}$

Substituting the given values into the equation:

$\text{Displacement}=\sqrt{{10}^2+{20}^2}$

$\text{Displacement}=\sqrt{100+400}$

$\text{Displacement}=\sqrt{500}$

Step 3: Calculate the final value
Taking the square root of 500:

$\text{Displacement}\approx 22.36\text{m}$

Approximating to the nearest option provided in the question, the value 22.36 m is closest to 22.5m.