Electrons- conservation of energy - electric potential

[mussgo]

An Electron is Projected An electron is projected with an initial speed of 2.4 x10^5 m/s directly toward a proton that is fixed in place. If the electron is initially a great distance from the proton, at what distance from the proton is the speed of the electron instantaneously equal to twice the initial value?


im having a lot of trouble with this problem i don't even know how to approach it can anyone pls help me to get started u..u

 

[Dick]

The sum of the kinetic energy (1/2)mv^2 of the electron plus it's potential energy in the field of the proton k*(-e)*(e)/r is a constant (note potential energy is negative!). At large r essentially all of the energy is kinetic. Find that. Now find the energy when v is doubled. At what value of r does the total energy balance?