a woman walks 2 km due east and then walks 4 km in the direction 30 degrees north of east. what is her magnitude of displacement from her starting point?

7,72

To find the magnitude of displacement, we need to determine the total distance and direction that a person has moved from their starting point. In this scenario, a woman walks 2 km due east (which we'll call the x-direction) and then walks 4 km in the direction 30 degrees north of east.

First, let's break down the two components of the woman's displacement:
1. The displacement in the x-direction: This is a straight line distance of 2 km in the east direction.
2. The displacement in the y-direction: This is the distance she walked north of the east direction. Since the angle is given as 30 degrees, we can use trigonometry to find the component in the y-direction. The formula to find the y-component is given by y = distance * sin(angle). So, the y-component is y = 4 km * sin(30 degrees).

Now, let's calculate the y-component:
y = 4 km * sin(30 degrees)
y = 4 km * (0.5) (using the value of sin(30 degrees) = 0.5)
y = 2 km

Therefore, the y-component of the displacement is 2 km.

Finally, we can find the magnitude of the displacement using the formula: magnitude of displacement = sqrt(x^2 + y^2), where x is the displacement in the x-direction and y is the displacement in the y-direction.
Magnitude of displacement = sqrt((2 km)^2 + (2 km)^2)
Magnitude of displacement = sqrt(4 km^2 + 4 km^2)
Magnitude of displacement = sqrt(8 km^2)
Magnitude of displacement ≈ 2.83 km (rounded to two decimal places)

Hence, the woman's magnitude of displacement from her starting point is approximately 2.83 km.