Relative Velocities: Plane Displacement from City in 2h Time

[slpnsldr]

Homework Statement

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

Homework Equations

Plane is P wind is W Earth is E

V_PW=V_PE+V_WE

The Attempt at a Solution

re arrange to find that
V_PE=V_PW-V_WE
V_PE=248km/h

The only thing I don't understand is how to determine the new angle of the plane to the earth...

 

[rl.bhat]

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

 

[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.

 

[slpnsldr]

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

 

[benhou]

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

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