A person can jump 1.5m on the Earth. 

How high could the person jump on a planet
having the twice the mass of the earth and twice the
radius of the earth? 



Let the mass of the earth be M and the radius of the earth be R. 

We are using the fact that the height to which the person will
be able to jump is inversely proportional to the
acceleration due to gravity. This gives us 



Recall that g is given by 



So, in this case, we have, for the earth 



and for the other planet 



Thus, we can write 



which, of course, reduces to the satisfyingly simple 



We therefore conclude that, assuming the
person could launch him/her self at the same initial speed she/he
would be able to jump twice as high on the other planet... this also
assumes that the spacesuit doesn't get in the way too much! 


