How Do You Calculate the Initial Speeds of Two Electrons in a Collision?

[Millacol88]

Homework Statement

Two electrons separated by a large distance are fired directly at each other. The closest approach in this head-on collision is 4.0 * 10^-14 m. One electron starts with twice the speed of the other. Assuming there is no deflection from the original path, determine the initial speed of each electron.

Homework Equations

E_e = kq₁q₂ / r
E_k = 1/2 mv²

The Attempt at a Solution

I'm really lost as to how to start this. It must have something to do with electrical and kinetic energy but other than that I am mystified as to how to solve this.

 

[technician]

My first step would be to calculate the potential of 2 electrons at the given separation (equation 1)
The total KE would then be equal to this as the next step

 

[Millacol88]

OK, so I'm getting the velocities as 1.0 * 10⁸ m/s and 5.0 * 10⁷ m/s. I'm pretty confident about this but the textbook only gives one answer (5.3 *7 10) m/s. There should be two velocities as an answer, so I think that must be an error. Is my answer correct?

 

[cupid.callin]

Homework Statement

Two electrons separated by a large distance are fired directly at each other. The closest approach in this head-on collision is 4.0 * 10^-14 m. One electron starts with twice the speed of the other. Assuming there is no deflection from the original path, determine the initial speed of each electron.

Homework Equations

E_e = kq₁q₂ / r
E_k = 1/2 mv²

The Attempt at a Solution

I'm really lost as to how to start this. It must have something to do with electrical and kinetic energy but other than that I am mystified as to how to solve this.

OK, so I'm getting the velocities as 1.0 * 10⁸ m/s and 5.0 * 10⁷ m/s. I'm pretty confident about this but the textbook only gives one answer (5.3 *7 10) m/s. There should be two velocities as an answer, so I think that must be an error. Is my answer correct?

I suppose yes, your answers are correct !