# Airplane's motion relative to the ground involving wind speed

## 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?

## 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 Im 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

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haruspex
Homework Helper
Gold Member
(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.

OK thanks..but y-component of plane's speed relative to the wind, (V_y)_PW would be 0 wouldnt 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 Ive even set up equation correct because thats what I think alot of the problem is about.
thanks

haruspex
Homework Helper
Gold Member
(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
?

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