# Homework Help: Relative velocities

1. Mar 15, 2010

### slpnsldr

1. The problem statement, all variables and given/known data
The wind is blowing at 72km/h south relative to the earth, and a plane is traveling 320km/h (28 degrees south of west relative to the wind) directly above a city. give displacement from the city in 2h time

2. Relevant equations
Plane is P wind is W earth is E

VPW=VPE+VWE

3. The attempt at a solution

re arrange to find that
VPE=VPW-VWE
VPE=248km/h

The only thing I dont understand is how to determine the new angle of the plane to the earth...

2. Mar 15, 2010

### rl.bhat

Velocities are vectors. You cannot add or subtract them directly.

3. Mar 15, 2010

### benhou

Hi slpnsldr. Your formula was incorrect. It should look like this
$$\vec{_{p}V_{E}}=\vec{_{p}V_{w}}+\vec{_{w}V_{E}}$$

Notice when you add these relative velocities, the subscript "w" cancel each other out. And that is the only trick to it.

4. Mar 15, 2010

### slpnsldr

ok, ive figured out my displacement.. but im still unclear about how to find the planes new angle
somethign to do with the sine law?

5. Mar 15, 2010

### benhou

Oh, that might be hard to explain without a diagram. Maybe you need to include a diagram.