Final answer:
The distance of closest approach between two protons can be found using energy conservation; the total initial kinetic energy of the two protons is converted into electrostatic potential energy at the point of closest approach. Without specific values, a numerical answer cannot be calculated.
Step-by-step explanation:
To determine the distance of closest approach between two protons moving directly toward each other, we employ the conservation of energy. When the protons are far apart, their potential energy is low, and kinetic energy is at its highest with the given initial speeds. As they approach each other, kinetic energy decreases while the electrostatic repulsive potential energy increases since like charges repel each other. At the point of closest approach, all kinetic energy will have been converted into potential energy.
We start by using the formula for kinetic energy, KE = (1/2)mv², where 'm' represents mass and 'v' their initial speed. For electrostatic potential energy (PE) between two point charges, we use the formula PE = k(q1q2)/r, where 'k' is Coulomb's constant, 'q1' and 'q2' are the charges of the protons, and 'r' is the separation distance. At the point of closest approach, the total initial kinetic energy of both protons will be equal to the potential energy.
Since we do not have the actual values for the proton's charge and mass, nor do we have a specific energy conservation relationship provided in the question, it is not possible for me to calculate an exact numerical answer.