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**Hint:**escape velocity of earth 11.2$km/\sec $. The escape velocity depends only on the mass and size of the object from which something is trying to escape. The escape velocity from the Earth is the same for a pebble as it would be for the Space Shuttle.

**Complete step by step answer:**

let the mass of earth be ${M_{earth}}$ and the mass of planet be${M_{planet}}$.

According to the question we know that ${M_{planet}} = 8{M_{earth}}$

Let radius of earth be ${r_{earth}}$and radius of the planet be ${r_{planet}}$

According to the question we know that ${r_{planet}} = 2{r_{earth}}$

Equation to calculate the escape velocity of a planet. ${v_{escape}} = \sqrt {\dfrac{{2G{M_{PLANET}}}}{{{R_{planet}}}}} $

Where G is gravitational G = Newton's universal constant of gravity$6.67 \times {10^{ - 11}}N/{m^2}/k{g^3}$

M= mass of the planet; R = radius of the planet.

So to find the escape velocity for our planet.

${v_{escape}} = \sqrt {\dfrac{{2G8{M_{earth}}}}{{2{R_{earth}}}}} $

${v_{escape}} = (\sqrt {\dfrac{8}{2}} ) \times \sqrt {\dfrac{{2G{M_{earth}}}}{{{R_{earth}}}}} $

We already know that the escape velocity of earth is 11.2km/sec.

${v_{escape}} = \sqrt {\dfrac{8}{2}} \times 11.2$

$\therefore {v_{escape}}= 22.4km/\sec $

**The escape velocity of our new planet will be 22.4 km/sec.**

**Note:**Other method: We can solve this question by equating the ratio of planet earth and our new planet.

So to find we know

${v_{escape}} = \sqrt {2gR} $

If mass of the planet is 8 times that of earth

$\dfrac{{{v_{planet}}}}{{{v_{earth}}}} = \sqrt {\dfrac{{{M_{planet}}}}{{{M_{earth}}}} \times \Rightarrow\dfrac{{{\operatorname{R} _{earth}}}}{{{R_{planet}}}}} $

$

\Rightarrow\dfrac{{{v_{planet}}}}{{{v_{earth}}}} = \sqrt {\dfrac{{8{M_{earth}}}}{{{M_{earth}}}} \times \Rightarrow\dfrac{{{R_{earth}}}}{{2{R_{earth}}}}} \\

$

$\Rightarrow\dfrac{{{v_{planet}}}}{{{v_{earth}}}} = 2$

$\Rightarrow{v_{planet}} = 2{v_{earth}}$

$\Rightarrow {v_{planet}} = 2 \times 11.2km/\sec $

$

\therefore{v_{planet}} = 22.4km/\sec \\

$

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