A plane flies from base camp to Lake A, 260 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 150 km at 30.0° west of north from Lake A. Graphically determine the distance and direction from Lake B to the base camp.

Distance :

Direction :

To graphically determine the distance and direction from Lake B to the base camp, we can follow these steps:

1. Start by drawing a diagram with Lake A at the origin (base camp) and Lake B located according to the given data.

2. Draw a vector representing the initial flight from base camp to Lake A. This vector should have a magnitude of 260 km and a direction 20.0° north of east. Label this vector as "Vector A".

3. From the tip of Vector A, draw another vector representing the flight from Lake A to Lake B. This vector should have a magnitude of 150 km and a direction 30.0° west of north. Label this vector as "Vector B".

4. To find the distance from Lake B to the base camp, draw a vector from the tip of Vector B back to the origin (base camp). This will represent the displacement from Lake B to the base camp. Label this vector as "Vector C".

5. To determine the magnitude of Vector C (distance), you can use the Pythagorean theorem. The magnitude of Vector C is equal to the square root of the sum of the squares of the horizontal and vertical components of Vector C.

6. To find the direction of Vector C, you can use trigonometry. Calculate the angle between Vector C and the horizontal axis (east) using the arctangent function. This will give you the direction in degrees.

The distance and direction can be determined by measuring the length and angle of Vector C using a ruler and a protractor on the drawn diagram.