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The baseball pitcher on an asteroid

  1. Sep 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A baseball pitcher can throw a fastball at a speed of 150 km/hr. What is the largest size spherical asteroid of density rho=3 g/cm^3 from which he can throw the ball fast enough that it:

    (a) escapes from the asteroid into heliocentric orbit?
    (b) rises to a height of 50 km?
    (c) goes into a stable orbit about the asteroid?

    2. Relevant equations
    i think...
    KE = 1/2mv^2 (kinetic energy)
    PE = GmM/r (potential energy, gravitational)
    Fc = mv^2/r (centrifugal force)
    Fg = GmM/r^2 (gravitational force)

    3. The attempt at a solution
    v = 150 km/hr ~ 42 m/s
    rho = 3 g/cm^3 = 3000 kg/m^3

    M = rho*V
    V = 4/3*pi*r^3

    (a) make KE = PE and solve for r, which i get r = v*sqrt(3/8*pi*rho*G) = 32439 m

    (b) not sure...

    (c) make Fc = Fg and solve for r, which i get r = v*sqrt(23/4*pi*rho*G) = 45876 m

    Did I do (a) and (c) correctly, and how should I approach (b)? Many thanks!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 11, 2012 #2
    For part (b) you should use the equation PE=mgh (where m is the mass of the object, g is the gravitational force on the object, and h is the height of the object) You know what the initial kinetic energy is, and that at the peak of the throw; the potential energy will be equal to the the initial potential energy.
    I'm afraid that I'm not sure about the other two though...
  4. Sep 12, 2012 #3
    Re: A baseball pitcher on an asteroid

    B uses pretty much the same method as the other two, you just need to find the PE of the baseball at 50 km
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