What is the minimum initial velocity $($with respect to the earth$)$ required for an object to escape from the solar system? Take the orbital motion of the earth into account $($but ignore the rotation of the earth, and ignore the other planets$).$ You are free to choose $($wisely$)$ the firing direction. Make the $($good$)$ approximation that the process occurs in two separate steps: first the object escapes from the earth, and then it escapes from the sun $($starting at the radius of the earth's orbit$).$ Some useful quantities are given in the solution to Problem $5\mathrm{.}11$; also, the orbital speed of the earth is about $30$ km$/$s$.$ Hint: a common incorrect answer is $13\mathrm{.}5$ km$/$s$.$