After flying for 15 min in a wind blowing 42 km/h at an angle of 30° south of east, an airplane pilot is over a town that is 50 km due north of the starting point. What is the speed of the airplane relative to the air?

This is a vector equation. I would do it graphically. vector from start to end, minus the wind vector, is equal to speed of airplane.

To find the speed of the airplane relative to the air, we need to consider the vector equation you mentioned. Let's break down the problem step by step:

1. Start by drawing a diagram to represent the situation. Draw a vector from the starting point to the ending point, indicating the flight path of the airplane. Label this vector as "Airplane Path" or "Airplane Vector."

2. Since there is a wind blowing at an angle of 30° south of east, draw another vector to represent the wind direction. Label this vector as "Wind Vector" and make sure it is 30° south of east.

3. The airplane's speed relative to the air can be represented by the difference between the "Airplane Path" vector and the "Wind Vector." Subtract the "Wind Vector" from the "Airplane Path" vector and label the resulting vector as "Airplane Speed."

4. Measure the magnitude of the "Airplane Speed" vector using a ruler or scale. This will give you the speed of the airplane relative to the air.

5. Convert the distance measurement on the diagram to kilometers (since we know that the town is 50 km north of the starting point). This will help us find the magnitude of the "Airplane Speed" vector in km/h.

Now, let's apply the steps to solve the problem:

1. Draw the "Airplane Path" vector from the starting point to the town, which is 50 km north of the starting point.

2. Draw the "Wind Vector" at 30° south of east, with a length representing the speed of the wind (42 km/h).

3. Subtract the "Wind Vector" from the "Airplane Path" vector to obtain the "Airplane Speed" vector. This represents the airplane's speed relative to the air.

4. Measure the magnitude of the "Airplane Speed" vector on the diagram.

5. Convert the magnitude of the "Airplane Speed" vector to km/h based on the scale used on the diagram. This will give us the answer to the question.

After following these steps, you should be able to find the speed of the airplane relative to the air.