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avatar+956 

An airplane is heading north with an airspeed of 400 km/h. The plane encounters a wind from the east at 100 km/h. What is the magnitude of the resultant ground velocity? 

 

a) 387 km/h 

b) 400 km/h

c) 412 km/h 

d) 500 km/h 

 

So this got me a bit confused: I did: 

√[ (400)^2+(100)^2 ] = 412 km/h

HOWEVER 

√[ (400)^2-(100)^2 ] = 387 km/h

 

Which one is correct? I think it's C though 

 May 23, 2018
 #1
avatar+99580 
+2

Let  the airplane be represented by the  vector     < 0, 400 >

Let the wind be represented  by the vector    < -100, 0 >

 

The components of the  airplane  vector  are     400 cos 90  = 0     and   400 sin 90  = 400

The components of the wind vector  are   -100 cos 180  = 100    and -100 sin180  = 0

 

So....the resultant vector  is found as    

 

sqrt [ ( 0 + 100 )^2  + ( 400 + 0 )^2  ] = 

 

sqrt  [ 10000 + 160000 ] =

 

sqrt [ 170000]  = 

 

412.3 km / h   =  412 km/h  [rounded ] 

 

 

cool cool cool

 May 23, 2018

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