Airplane's motion relative to the ground involving wind speed

[sp3sp2sp]

Homework Statement

Plane is 300miles E of chicago and it leaves flying east at 500mph. Wind is blowing 50mph south.
What is planes ground speed?
Where is plane 0.6 hours later when pilot expects to land in cleveland?

Homework Equations

The Attempt at a Solution

This is how I set it up
I want PG, which is plane speed relative to ground
W = wind, P = plane, G = ground

(V_x)_PG = (V_x)PW + (V_x)WG
(V_y)_PG = (V_y)PW + (V_y)WG

So now I am filling in the values and it doenst look right, so I wanted to check this preliminary step

(V_x)_PG = (V_x)PW + (V_x)WG --> 500mph = (V_x)PW + 0mph
(V_y)_PG = (V_y)PW + (V_y)WG --> 0mph = (V_y)PW + (-50mph)

I think (V_x)PW should also be 500mph and (V_y)PW should = +50mph to make the equations correct, but the 2 equations are not telling me anything I didnt already know from the question stem.

Is this correct so far?
thanks for any help

 

[haruspex]

(V_y)_PG = (V_y)PW + (V_y)WG --> 0mph = (V_y)PW + (-50mph)

I would take "flying east" as referring to the heading, i.e. direction relative to the wind.

 

[sp3sp2sp]

OK thanks..but y-component of plane's speed relative to the wind, (V_y)_PW would be 0 wouldn't it? Because it travels east there is no movement in y direction, so equation for y should be
(V_y)_PG = (V_y)PW + (V_y)WG
0mph = +50mph + - 50mph

I was hoping to get opinion if I've even set up equation correct because that's what I think a lot of the problem is about.
thanks

 

[haruspex]

(V_y)_PW would be 0

Yes, so why have you again written

(V_y)_PG = (V_y)PW + (V_y)WG
0mph = +50mph + - 50mph

?

 

[sp3sp2sp]

Can someone please walk me through this problem? I am getting more and more confused every time I try to work the problem. Thanks in advance

 

[haruspex]

Can someone please walk me through this problem? I am getting more and more confused every time I try to work the problem. Thanks in advance

Fill in the values in your equation

(V_y)_PG = (V_y)PW + (V_y)WG

using your new understanding that V_y,PG is unknown and

, (V_y)_PW would be 0