"TOTAL DISTANCE TRAVELED WILL BE = 1.5 + 2 + 4.5 = 8 m FINAL DISPLACEMENT WILL BE = We can directly make a diagram for 6 m east and 2 m south, the resultant will be same. Final Displacement = √ ( 6 square + 2 square ) = √ ( 36 + 4 ) = √40 m ANSWER = (a) 8 m (b) √40 m

Resultant Displacement:

To find the resultant displacement, we need to calculate the net distance and direction of the man's travel.

Step 1: Calculate the distance traveled in the east direction:
The man travels a distance of 1.5 m towards the east. This is his initial displacement in the east direction.

Step 2: Calculate the distance traveled in the south direction:
Next, the man travels 2.0 m towards the south. This is his displacement in the south direction.

Step 3: Calculate the distance traveled in the east direction again:
Finally, the man travels 4.5 m towards the east. This is his displacement in the east direction.

Step 4: Calculate the net displacement:
To find the net displacement, we need to add the displacements in the east and south directions. Since the east and west directions are in opposite directions, we can subtract the distance traveled west from the distance traveled east.

Net east displacement = 1.5 m + 4.5 m = 6.0 m (east)
Net south displacement = 2.0 m (south)

To calculate the resultant displacement, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Step 5: Apply the Pythagorean theorem:
Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement (R) as follows:

R^2 = (Net east displacement)^2 + (Net south displacement)^2
R^2 = (6.0 m)^2 + (2.0 m)^2
R^2 = 36.0 m^2 + 4.0 m^2
R^2 = 40.0 m^2

Taking the square root of both sides, we get:

R = √40.0 m^2
R ≈ 6.32 m (rounded to two decimal places)

Step 6: Determine the direction of the resultant displacement:
To find the direction of the resultant displacement, we can use trigonometry. The tangent of the angle between the resultant displacement and the east direction is given by:

tan θ = (Net south displacement) / (Net east displacement)
tan θ = 2.0 m / 6.0 m
tan θ ≈ 0.333

Taking the inverse tangent (tan^-1) of both sides, we get:

θ ≈ 18.43°

Therefore, the resultant displacement is approximately 6.32 m towards the east at an angle of 18.43° south of east.

Plzz accept my chat request