Magnetic force on a moving charge particle with friction force acting on it

[siddscool19]

Homework Statement

A "q" charge particle is moving along +y axis with velocity V₀ starting from Origin. A friction force is acting on the charge particle " f= -(alpha)V(Vector) ".A constant magnetic field of magnitude B₀ acting along +Z axis. The mass of the particle is m. Find the x co-ordinate of the particle when it stops.

Homework Equations

The Attempt at a Solution

I Have found that the total path moved by the particle is mV₀/(alpha)

But I don't know how to find x coordinate with it.

 

[hikaru1221]

There is a quick way to solve this problem: write down the Newton 2nd law equation in vector form and integrate it

 

[IEVaibhov]

I have solved the problem. I am just too lazy to type the WHOLE thing out here. The solution is kind of long. Basically, get the general velocity along X axis and Y axis as a function of time.
To obtain this, in the penultimate step, you will get a differential equation that you will have to solve using Complex numbers.
In the end, the velocities will be something of the type v0*[e(^(-constant))]*cos(wt), where w is the angular frequency.

 

[cupid.callin]

I have solved the problem. I am just too lazy to type the WHOLE thing out here.

You are not even allowed to write whole solution. you can just give hints.