asteroid collision?

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asteroid collision?

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• you have to use conservation of linear momentum on this problem

  momentum (p)=mass x velocity so the original momentum is

  p=40m where m is any arbitrary mass

  you know that this linear momentum must be conserved after the collision so the combined momentum of the two rocks after should equal this amount. Set up a system of equations using the components of each momentum

  x direction

  40m=mv(a)cos30+mv(b)cos(-45)

  you can cancel the masses in every term and be left with

  40=v(a)cos30+v(b)cos(-45)

  this is the total momentum in the x-direction.

  you need another equation so lets take the y components

  it initially has no momentum in the y direction so

  0=v(a)sin30+v(b)sin(-45)

  so your system of equations looks like this

  .5v(a)-.7071v(b)=0

  .8660v(a)+.7071v(b)=40

  you can add these two equations to solve for v(a) and you get

  1.366v(a)=40 so

  v(a)=29.3 m/s

  plug this in to either equation to get v(b)=

  20.7 m/s

  for the third part of the question find the kinetic energy of the original asteroid and the kinetic energy of the two final asteroids added together.

  so initial kinetic energy is

  1/2mv^2=

  .5m(40)^2

  and final kinetic is

  .5m(29.3)^2+.5m(20.7)^2

  so you get

  800m for initial

  and

  429.245+214.245=

  643.49 for final

  you need to find the fraction lost so subtract and get

  800-643.49=

  156.51

  find out what percent of the original this amount is

  156.51/800=.196 or

  19.6%

• 1. There are no “huge” asteroids. The largest asteroid is Ceres, which is 952 km. in diameter. 2. Most asteroids are between the orbts of Mars and Jupiter, but very few get as far out as Jupiter’s orbit itself, so the chances of collision with an asteroid are slim. 3. At least two comets have collided with Jupiter in the past 20 years. They caused temporary scars in Jupiter’s upper atmosphere, but had no lasting effects. 4. The only other large objects n the Solar System are planets, and they are all in stable orbits and never come anywhere close to Jupiter. 5. Jupiter is not large enough to sustain nuclear fusion.

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