A plane travelling a velocity of 100km/h to south encounters aside wind blowing at 25km/h to the west what is its velocity to an observer on the ground?

To determine the velocity of the plane to an observer on the ground, we need to use vector addition.

First, let's represent the velocity of the plane traveling south as a vector in the negative y-direction. We'll call this vector V1 and its magnitude is 100 km/h.

Next, let's represent the velocity of the wind blowing west as a vector in the negative x-direction. We'll call this vector V2 and its magnitude is 25 km/h.

To find the resultant velocity, we need to add these two vectors together. We can do this by using the Pythagorean theorem and trigonometry.

The magnitude of the resultant velocity can be calculated as follows:

Resultant magnitude = √(V1^2 + V2^2)

In this case, V1 = 100 km/h and V2 = 25 km/h.

Resultant magnitude = √(100^2 + 25^2) = √(10000 + 625) = √10625 ≈ 103.06 km/h

The direction of the resultant velocity can be calculated using the inverse tangent function:

Resultant direction = arctan(V2/V1)

In this case, V1 = -100 km/h and V2 = -25 km/h.

Resultant direction = arctan(-25/-100) = arctan(0.25) ≈ 14.04°

Therefore, the velocity of the plane to an observer on the ground is approximately 103.06 km/h in a direction of 14.04° west of south.