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Homework Help: Gravity and Vertical Jump Problem

  1. Sep 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Imagine that you are prospecting for rare metals on a sperical asteroid composed mostly of iron (which density is 7800 kg/m^3). The radius of the asteroid is about 4.5 km. You've left your spaceship in a circular orbit 400 meters above the asteroid's surface and gone down to the surface using a jet pack. Is it possible for you to simply jump high enough in this situation to get back to the spaceship?

    2. Relevant equations
    The kinetic energy produced by my legs would be equal to K(me)=(60kg)(3.1m/s)^2(1/2)

    area of sphere=(4(3.14)r^3)/3

    V(me to ship)=-G(M(ship)M(asteroid)/r)
    G=6.67 a 10^-11
    mg=1000 kg

    3. The attempt at a solution
    K(me)=93 J

    area of sphere=3.8x10^11 m^3

    mass of asteroid=3x10^15kg

    V(me to ship from asteroid)=-(6.67x10^-11 J*m/kg^2)[(1000kg*3x10^15kg)/400m)
    =-500,000 J (I do not think this number is reasonable)

    My legs could produce almost 1200 J which is significantly less than 500,000 J. Therefore, there is no way I could jump back to my ship if my pack broke.
  2. jcsd
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