SOLUTIONS TO EXERCISE 20

The first mini-asteroid has a momentum  p = mv = 15 * 15 = 225 kg m/s east.

The second mini-asteroid has p = mv = 15 * 30 = 450 kg m/s west,
  or -450 kg m/s east (the negative is important, because direction matters).

(a) According to Newton's First Law, the combined momentum of the two mini-
asteroids will be the same before the collision as after the collision.  Thus,

    total p = 225 + (-450) = -225 kg m/s east.
    total m = 15 + 15 = 30 kg.

    So since p = mv, v = P/m = -225 / 30 = -7.5 m/s east, or 7.5 m/s west.

(b) From part (a) above, the total p = -225 kg m/s east.
    One of the asteroids now has momentum p = mv = 15 * 25 = 375 kg m/s west,
      or -375 kg m/s east.
    Thus, the other asteroid now has p = (-225) - (-375) = 150 kg m/s east.
    That asteroid is thus moving at v = P/m = 150 / 15 = 10 m/s east.