Relative Velocities: Plane vs Air & Ground

[physstudent1]

Homework Statement

A small plane flies at 120km/h over the end of a runway along the axis of the runway. There is a crosswind, exactly 90 degrees to the direction of the runway, blowing at 50km/h. The speed of the plane with respect to the air is:

130km/h
50km/h
120km/h
need more info
70km/h

Homework Equations

The Attempt at a Solution

I set up the equation:

V(p/g) ( plane respect to ground ) = V(p/a) (plane respect to air) + V(a/g) (air respect to ground)

p/g = 120 a/g =50

120 = 50 +x
sqrt(120^2 - 50^2) = x ?

this gives 109 km/h though which is not a choice, did I do something wrong?

 

[Astronuc]

sqrt(120^2 - 50^2)

Why this?

The plane is flying straight with the runway at 120 mph, and the plane has to be moving through the air. The wind is blowing cross-wise so the planes velocity in the air must be the vector sum of its velocity and the winds velocity.

 

[Mindscrape]

Why are you taking the square root? Everything is in the same direction.

 

[physstudent1]

how is everything in the same direction if the wind is blowing perpindicular to the runway

 

[physstudent1]

so it is 130?

the reason i was subtracting was because I tried putting it into the equation

V p/a = V p/b + V b/a

and i got

120 = x + 50

 

[Mindscrape]

Oh, I guess I don't know what crosswise means. I thought it meant across the cross section. Why not just say perpendicular, or if they really want to be fancy, orthogonal. I guess I am still an idiot for not even reading the 90 degree part, my bad. Yes, it would be 130.

Do the vector diagram, and it should be pretty apparent.