An airplane propels itself eastward with speed v. A crosswind with speed u is directed at...

An airplane propels itself eastward with speed v. A crosswind with speed u is directed at an angle θ (0 < θ < π) north of east. What is the distance travelled by the plane after a time t?

Expert Solution

Let positive x be along east and positive y be along north.

Then,velocity of airplane relative to air = v

Velocity of wind = u cos + u sin

So, net velocity of the airplane = velocity of airplane relative to air+velocity of wind

= (v+ucos)+(usin)

Magnitude of velocity = [(v+ucos)^2+(usin)^2]^0.5

= [v^2+(ucos)^2+2uvcos+(usin)^2]^0.5

= [u^2+v^2+2uvcos]^0.5

So, distance= (magnitude of velocity)*time = [(u^2+v^2+2uvcos)^0.5]*t

genius_generous answered 1 year ago

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