A car drives 100 meters at 30 degrees north of east, stops, turns to an angleof 210 degrees from the east, and then drives another 60 meters. What is the magnitude of the total displacement?

To find the magnitude of the total displacement, we first need to break down the car's motion into its components.

Step 1: Car drives 100 meters at 30 degrees north of east.
In this step, the car's motion can be represented as a vector with a magnitude of 100 meters and an angle of 30 degrees. We can break down this vector into its eastward (x) and northward (y) components using trigonometry.

x-component = 100 meters * cos(30 degrees)
y-component = 100 meters * sin(30 degrees)

Step 2: Car stops and turns to an angle of 210 degrees from the east.
In this step, the car changes its direction. The change in direction can be represented as an angle of 210 degrees from the east.

Step 3: Car drives another 60 meters.
In this step, the car moves 60 meters in its new direction.

Now, let's calculate the new displacement of the car.

x-displacement = x-component from step 1 + 60 meters * cos(210 degrees)
y-displacement = y-component from step 1 + 60 meters * sin(210 degrees)

To find the magnitude of the total displacement, we use the Pythagorean theorem.

total displacement = √(x-displacement^2 + y-displacement^2)

Now, let's plug in the values and calculate the answer.