A spherically symmetric asteroid has a radius R $=500$ km$.$ The acceleration due to

gravity at its surface has magnitude gA $=3\mathrm{.}00$ m$/$s$2.$

a$.$ Find the escape speed vesc of the asteroid. Show and explain your work.

c$.$ A rock is ejected radially outward from the surface of the asteroid with a speed of

$1\mathrm{.}00$ km$/$s$.$ Find the maximum distance from the surface that it reaches.

d$.$ A rock is dropped from rest at a height of $1\mathrm{.}00103$ km above the surface of the

asteroid. Find its speed when it strikes the surface.