An astronaut becomes stranded outside the spacecraft after her tether breaks. Her velocity relative to the spacecraft is zero. Her mass, with her EVA suit and $17\mathrm{.}6-kg$ tool bag, is $128\mathrm{.}4$ kg $.$

a$.$ In order to return to the ship she throws the tool bag directly away from her and the ship at a velocity of $2\mathrm{.}15\frac{m}{s}.$ Why does she do this?

b$.$ Calculate her velocity after throwing the bag.

c$.$ How many minutes does does it take her to reach the ship, which is located $58\mathrm{.}4$ m away?