Town A lies 20 km north of town B. Town C lies 13 km west of town A. A small plane flies directly from town B to town C. What is the displacement of the plane.

To find the displacement of the plane, we need to determine the straight-line distance between town B and town C.

First, let's determine the distance between town A and town C. We know that town C lies 13 km west of town A.

Next, we need to find the total distance traveled by the plane. Since town A lies 20 km north of town B, the plane first needs to fly 20 km north from town B to reach town A. From there, it needs to travel an additional 13 km west to reach town C.

To calculate the distance traveled by the plane, we can combine the distances traveled in both the north and west directions using the Pythagorean theorem.

Using the Pythagorean theorem, the distance traveled can be calculated as follows:

Distance^2 = (20 km)^2 + (13 km)^2

Distance^2 = 400 km^2 + 169 km^2

Distance^2 = 569 km^2

Taking the square root of both sides gives us:

Distance = √(569 km^2)

Distance ≈ 23.85 km

Therefore, the displacement of the plane (the straight-line distance between town B and town C) is approximately 23.85 km.