What is the escape speed on a spherical asteroid whose radius is $575$ km and whose gravitational acceleration at the surface is $3\mathrm{.}1$ m$/$s$2?$

m$/$s

$($b$)$ How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of $1000$ m$/$s$?$

m

$($c$)$ With what speed will an object hit the asteroid if it is dropped from $1000$ km above the surface?