Calculating New Northward Speed of Air Parcel

[Mearskii]

Homework Statement

A parcel of air initially moves northward at a speed of 10 m/s at 45°S. After two hours, determine the new northward speed.

Homework Equations

Energy of a parcel= u^2+v^2

The Coriolis force accelerates a parcel such that, du/dt=fv and dv/dt=-fu
where f=2Ωsin\varphi \varphi =latitude and Ω=angular velocity of earth

The Attempt at a Solution

My first question about this problem is in regards to what it is asking for. It says to find the new northward speed of the parcel, however the Coriolis force only changes direction, not speed. So I then considered that the northward component of speed would change and that must be what the question is asking for. But then I thought about how speed is a scalar, not a vector, so there would be no "northward component" of speed because there simply aren't speed vectors. Please correct me if I'm wrong.

 

[cepheid]

Welcome to PF,

So you're just hung up on terminology? The "northward speed" means the speed in the northward direction, which is the magnitude of the northward component of the velocity.