An airplane flies due south at 185 km/h relative to the air. There is a wind blowing at 68 km/h to the east relative to the ground. What are the plane's speed and direction relative to the ground?

I can check your work on this.

(a+b)2

To find the airplane's speed and direction relative to the ground, we can use vector addition.

First, let's break down the given information into their respective vectors:

1. Airplane's velocity relative to the air:
- Speed: 185 km/h
- Direction: Due south (opposite to the north direction)

2. Wind's velocity relative to the ground:
- Speed: 68 km/h
- Direction: East (perpendicular to the north-south direction)

Now, let's find the resultant vector by adding the two vectors together.

To add the vectors, we will use the concept of vector addition. It involves adding the vertical (north-south) and horizontal (east-west) components separately.

First, let's calculate the vertical component (north-south):

The airplane's velocity relative to the air is due south, so its vertical component is -185 km/h (negative because it is in the opposite direction to the north).

Next, let's calculate the horizontal component (east-west):

The wind's velocity is blowing to the east, perpendicular to the north-south direction. Therefore, it will have no influence on the airplane's east-west component. Hence, the horizontal component remains 0 km/h.

Finally, let's find the resultant vector:

The resultant vector will have two components: the vertical component (-185 km/h) and the horizontal component (0 km/h). Since the horizontal component is 0, the resultant vector will point straight south with a speed of -185 km/h (negative due to the opposite direction from north).

Therefore, the airplane's speed relative to the ground is 185 km/h, and its direction relative to the ground is due south.