Problem $1.$

A bow is drawn by Mete Gazoz, a Turkish Olympic winner archer, by a force of $300N,$ to the back by $0\mathrm{.}6m.$

$($a$)$Assuming the bow behaves like an ideal spring, what spring constant would allow the archer to make use of his full strength?

$($b$)$ What potential energy is stored in the bow when it is drawn?

$($c$)$Assuming the arrow has a mass of $30g,$ approximately what speed will it be fired at$?$