Consider an aircraft attempting to fly south at 600km/h encounters a head wind of 200km/h. Calculate its resultant velocity.

since the wind is from directly ahead, just subtract it:

600-200 = 400

60,000

To calculate the resultant velocity, we need to consider the effect of the headwind on the aircraft's velocity.

The headwind is opposing the aircraft's motion, which means it will reduce the aircraft's speed. The magnitude of the headwind is given as 200 km/h.

Since the aircraft is flying directly south at a speed of 600 km/h, its velocity can be represented as a vector pointing south with a magnitude of 600 km/h.

To find the resultant velocity, we need to subtract the magnitude of the headwind from the aircraft's velocity. This can be done using vector subtraction.

Let's break down the vector calculation step by step:

1. Start by drawing a vector that represents the aircraft's velocity of 600 km/h pointing south.

2. Then, draw a vector that represents the headwind of 200 km/h pointing north. Since the headwind is opposing the aircraft's motion, we represent it as a vector pointing in the opposite direction.

3. To subtract the headwind vector from the aircraft's velocity vector, place the tail of the headwind vector onto the head of the aircraft's velocity vector.

4. Draw a new vector connecting the tail of the aircraft's velocity vector to the head of the headwind vector. This new vector represents the resultant velocity.

5. The magnitude of the resultant velocity is the distance between the tail of the aircraft's velocity vector and the head of the headwind vector.

The resultant velocity vector represents the aircraft's actual movement, taking into account the effect of the headwind.

Now, to calculate the magnitude of the resultant velocity, we use the Pythagorean theorem:

Resultant velocity = sqrt((600 km/h)^2 + (200 km/h)^2)

Calculating this, we get:

Resultant velocity = sqrt(360,000 km^2/h^2 + 40,000 km^2/h^2) = sqrt(400,000 km^2/h^2) = 632.46 km/h (approximately)

Therefore, the resultant velocity of the aircraft is approximately 632.46 km/h in a direction slightly south of straight south, due to the effect of the headwind.