Suppose that you are stranded$-$your rocket engine has failed$-$on an asteroid of diameter $2$ miles, with density equal to that of the earth with radius $3,960$ miles. If you have enough spring in your legs to jump $3\mathrm{.}8$ 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

$36,680\frac{ft}{(s)}$

Select the correct choice below and fill in the answer box to complete your choice.

$($Type integers or decimals rounded to two decimal places as needed.$)$

Yes, you can blast off because the escape velocity of the asteroid, $\frac{ft}{s},$ is less than

A$.$ your initial velocity when jumping, $\frac{ft}{s}.$

No$,$ you cannot blast off because the escape velocity of the asteroid, $\frac{ft}{s},$ is greater B$.$ than your initial velocity when jumping, $\frac{ft}{s}.$