Calculating Plane Velocity with Wind: 200 km/h Airspeed, 50.0 km/h West Wind

[rhxoehwhfh]

The airspeed of a small plane is 200 km/h. The wind speed is 50.0 k/h from the west. Determine the velocity of the plane relative to ground if the pilot keeps the plane pointing to each of the following directions:
a) [E] b) [W] c) [N] d) [N400E]


I never learned this stuff but it is on my homework, can anyone give me formula to solve this problem please?..

 

[Astronuc]

This is a problem of vector addition.

The 200 km/h is the magnitude airspeed (speed of plane relative to the air) and the problem gives 4 orientations, which then defines that vector, to which one then adds the velocity of the wind.

Since the wind if from the west, it is moving toward the east, so take E as the + direction, and denote the unit vector as i. For the opposite direction, W, the vector would be -i. Similarly N would be +j or j and S would be -j.

Take part a. The plane if flying E at 200 km/h with respect to the air, and the air is moving E at 50 km/h. Adding the two vectors, one gets 200 i + 50 i = 250 i, so the plane is moving 250 km/h due E.

Now try the others.

See this reference - http://hyperphysics.phy-astr.gsu.edu/hbase/airpw.html

 

[rhxoehwhfh]

Thankyou very much sir