A pilot flies out of Cleveland and sets his compass due North. He maintains an airspeed of 250 km/hr. After 30 minutes he finds that the plane is 200 km north and 40 km west of the starting point. What is the velocity of the wind?

I've made my triangle and found the hypotenuse and the angles inside. I just don't know what's the next step to finding the wind velocity?

flying N at 250 km/h for 30 min should put him at 125 km N of the start

the wind has pushed him 75 km N and 40 km W in 30 min

so the wind is blowing 150 km/h N and 80 km/h W

Vw² = 150² + 80²

the tangent of the angle (west of north) is...8/15

To find the wind velocity, we need to break down the plane's movement into its components: the northward component due to the plane's airspeed, and the westward component due to the wind. Let's denote the velocity of the wind as Vw and the northward component of the plane's airspeed as Va.

1. Start by using the information given to solve for Va:
- We know that the plane is 200 km north in 30 minutes, so its northward component of the airspeed is Va = Distance / Time = 200 km / 0.5 hr = 400 km/hr.

2. Now, let's find the westward component of the plane's airspeed, Vw0:
- We know that the plane is 40 km west in 30 minutes, so its westward component of the airspeed is Vw0 = Distance / Time = 40 km / 0.5 hr = 80 km/hr.

3. Next, let's find the actual velocity of the plane (without considering the wind), Vp:
- We can use the Pythagorean theorem to find the hypotenuse of the triangle formed by the plane's movement, which is the actual velocity of the plane:
Vp² = Va² + Vw0² = (400 km/hr)² + (80 km/hr)² = 160,000 km²/hr².
Taking the square root of both sides, Vp ≈ 400 km/hr.

4. Finally, we can find the velocity of the wind, Vw:
- Since the velocity of the plane is the vector sum of the airspeed and wind velocity, we can use vector subtraction:
Vp = Va + Vw.
Rearranging the equation, we have Vw = Vp - Va = 400 km/hr - 400 km/hr = 0 km/hr.

Therefore, the velocity of the wind in this scenario is 0 km/hr.