A man walks 4m towards east and then turns 60degrees to his left and again walks for 4m calculate the net displacement
D = 4m[0o] + 4m[60o].
X = 4*Cos0 + 4*Cos60 = 6 m.
Y = 4*sin 0 + 4*sin = 60 = 3.46 m.
D = sqrt(X^2 + Y^2) = 6.93 m. Displacement.
6.925
To calculate the net displacement, we need to find the total distance and direction from the starting point to the ending point.
Let's break down the given information step by step:
1. The man walks 4m towards the east. This means he moves 4 meters in the east direction.
2. Then, he turns 60 degrees to his left. This means he changes his direction by turning counter-clockwise by 60 degrees.
3. Finally, he walks for 4m in the new direction after turning left.
Now, let's calculate the net displacement:
Step 1: The man walks 4m towards the east, so his displacement in this step is +4m in the east direction.
Step 2: The man turns 60 degrees to his left. This turn doesn't contribute to displacement since he remains at the same location.
Step 3: After turning left, he walks for 4m in the new direction. The displacement in this step depends on the angle between the new direction and the east direction.
Since the man turned 60 degrees to his left, the angle between the new direction and the east direction is 90 degrees - 60 degrees = 30 degrees. This means the new direction is 30 degrees north of east.
Using basic trigonometry, we can calculate the displacement in this step as follows:
Displacement = 4m * cos(30 degrees) = 4m * 0.866 = 3.464m
Step 4: The net displacement is the sum of the displacements in each step.
Net Displacement = 4m (east) + 3.464m (30 degrees north of east) = 7.464m (approximately)
Therefore, the net displacement of the man is approximately 7.464 meters.
total east ... 4 m + 4 cos(60º) m
total north ... 4 sin(60º) m