Suppose that you are

strandedlong dash$$your

rocket engine has

failedlong dash$$on

an asteroid of diameter

$3$

$$miles$,$ with density equal to that of the earth with radius

$3$ comma $960$

$3,960$

miles. If you have enough spring in your legs to jump

$4\mathrm{.}94\mathrm{.}9$

feet straight up on earth while wearing your space$$ suit, can you blast off from this asteroid using leg power$$ alone? Note that the escape velocity on Earth is about

$36$ comma $680$ StartFraction ft Over s EndFraction$36,680$fts$.$