Find v for Mars if the escape velocity for earth, Ve=11.2 km

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RPMACS

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The escape velocity v a spacecraft needs to leave the gravitational field of a planet varies directly as the square root of the product of the planet’s radius R and its acceleration due to gravity g. For Mars and Earth:

Rm=.533 Re (e is small lower) and gm (m is small lower) =.400 ge(e is small lower)

Find vm(m is small lower) for Mars if the escape velocity for earth, Ve =11.2 km/s

Help!
 
Perhaps someone else will follow, but I am not sure what all that means. But, by looking it up, the escape velocity of Mars is about 5 km/hr, as oppsoed to Earth's 11.2 km/hr. That is something to shoot for.
 
\(\displaystyle The \ escape \ velocity \ from \ a \ planet \ of \ mass \ M \ and \ radius \ R \ is \ given \ by\)

\(\displaystyle V_{escape} \ = \ \sqrt\bigg(\frac{2GM}{R}\bigg), \ where \ G \ is \ the \ universal \ constant \ of\ gravitation.\)

\(\displaystyle G \ = \ 6.67 (10^{-11})Nm^{2}/kg^{2}, \ note \ 1N \ = \ \frac{1kgm}{sec^{2}}, \ thank \ you \ Sir \ Isaac.\)

\(\displaystyle Now, \ the \ mass \ of \ Mars \ = \ 6.419(10^{23})kg \ and \ the \ radius \ of \ Mars \ = \ 3397km.\)

\(\displaystyle Ergo, \ Escape \ Velocity \ = \ \sqrt\bigg(\frac{2[6.67(10^{-11})Nm^{2}][6.419(10^{23})]kg}{3,397,000mkg^{2}}\bigg)\)

\(\displaystyle = \ \sqrt\bigg(\frac{2[6.67(10^{-11})Nm][6.419(10^{23})]}{3,397,000kg}\bigg)\)

\(\displaystyle = \ \sqrt \bigg(\frac{8.562946(10^{13})m^{2}}{3,397,000sec^{2}}\bigg) \ = \ 5020.69488193m/sec \ = \ 5.02km/sec\)
 
RPMACS said:
The escape velocity v a spacecraft needs to leave the gravitational field of a planet varies directly as the square root of the product of the planet’s radius R and its acceleration due to gravity g. For Mars and Earth:

Rm=.533 Re (e is small lower) and gm (m is small lower) =.400 ge(e is small lower)

Find vm(m is small lower) for Mars if the escape velocity for earth, Ve =11.2 km/s

Help!
Click to expand...

v = k?(Rg)
11.2 = k?(1•1) = k

v = 11.2?[(0.533)(0.400)] ? 5.17 km/s
 
\(\displaystyle \frac{V_m}{V_e}=\frac{V_m}{11.2}= \frac{\sqrt{(0.533R_e)(0.4g_e)}}{\sqrt{(R_e)(g_e)}}=\frac{\sqrt{0.533}\sqrt{0.4}\sqrt{(R_e)(g_e)}}{\sqrt{(R_e)(g_e)}}=\sqrt{0.533}\sqrt{0.4},\ hence\quad V_m=11.2\sqrt{0.533}\sqrt{0.4}\)
 
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