A pedestrian moves 5.7 kmeast and then 8 km

north.
Find the magnitude of the resultant dis-
placement vector.
Answer in units of km

To find the magnitude of the resultant displacement vector, we need to use the Pythagorean theorem.

First, let's draw a diagram to visualize the pedestrian's movement.

The pedestrian moves 5.7 km east, so we can represent this as a vector pointing to the right with a magnitude of 5.7 km.

Next, the pedestrian moves 8 km north, so we can represent this as a vector pointing upwards with a magnitude of 8 km.

To find the magnitude of the resultant displacement vector, we need to find the length of the hypotenuse of the right triangle formed by these two vectors.

Using the Pythagorean theorem, the magnitude of the resultant displacement vector (R) is calculated as follows:

R = sqrt((5.7 km)^2 + (8 km)^2)

R = sqrt(32.49 km^2 + 64 km^2)

R = sqrt(96.49 km^2)

R ≈ 9.822 km

Therefore, the magnitude of the resultant displacement vector is approximately 9.822 km.