Me, again...

Question

Please help me. Thank you.

Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph.

Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of motion.

Part II: What is the velocity vector of the plane?

Part III: What is the ground speed of the plane?


IV: Sketch the velocity vectors of the plane and the new direction of the plane on the axes below. Label the plane's original velocity as vplane, the wind velocity as vwind, and the resultant velocity as v.

Answer 1

well, I suppose we can say East is x direction, unit vector i
and
North is y direction, unit vector j

then Vplane north = 0 i + 200 j
and V wind east = -23 i + 0 j
(I assume they mean the plane is pointed north, not going north)
(I am assuming they mean blowing toward the west the way it is phrased. Usually we say where a wind is coming from, not the direction it is going to)

then
Vresultant = Vr = -23 i + 200 j
(That is the velocity vector of the plane)
that is quadrant 2
tan angle above x axis =200/23
so that angle is 83.4 degrees above -x axis

speed = sqrt(23^2+200^2)
= 201.3 mph