A proton is directed such that it comes within $1\mathrm{.}6{10}^{-15}m$ of a carbon nucleus.

$($a$)$ How much kinetic energy must the proton have initially to get this close to $($i$.$e$.,$ "collide" with$)$ the carbon nucleus?

$5\mathrm{.}4e6J$

$($b$)$ What is the corresponding speed of the proton?

$\frac{m}{s}$

$($c$)$ What potential would be needed to give the proton this much kinetic energy? Assume the target carbon nucleus is completely ionized $($missing all electrons$),$ and that the collision is head$-$on$.$

V