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Worksheet: Momentum in Two Dimensions

Q1:

A rocket of mass 200.0 kg in deep space moves with a velocity of ( 1 2 1 + 3 8 . 0 ) i j m/s. Suddenly, it explodes into three pieces. The first piece has a mass of 78.0 kg and moves at ( 3 2 1 + 2 2 8 ) i j m/s. The second piece has a mass of 56.0 kg moves at ( 1 6 . 0 8 8 . 0 ) i j m/s. Find the velocity of the third piece.

  • A ( 4 4 2 8 0 . 0 ) / i j m s
  • B ( 2 0 0 5 0 . 6 ) / i j m s
  • C ( 2 1 6 1 9 0 . 1 ) / i j m s
  • D ( 7 3 3 + 7 9 . 6 ) / i j m s
  • E ( 7 1 6 1 3 0 . 8 ) / i j m s

Q2:

Two billiard balls are at rest and touching each other on a pool table. The cue ball travels at 3.8 m/s along the line of symmetry between these balls and strikes them simultaneously. If the collision is elastic, after it has occurred.

What is the speed of the cue ball?

What is the speed of each of the other two balls? (They will have the same speed as each other.)

What is the size of the angle from the line of symmetry at which the two other balls move?

Q3:

A bowling ball of mass 5.50 kg moving at 9.00 m/s collides elastically with a bowling pin of mass 0.850 kg. The pin is scattered at an angle to the initial direction of the bowling ball at a speed of 15.0 m/s.

Calculate the magnitude of the final velocity of the bowling ball.

Calculate the angle from the initial direction of the bowling ball’s motion of the final velocity of the bowling ball.

Q4:

Three deer, DeerA, DeerB, and DeerC, all of mass 70.0 kg are standing on a flat rock of mass 2 . 0 × 1 0 2 kg that is on an ice-covered pond. A gunshot goes off and the deer scatter, with DeerA running at ( 1 5 + 5 . 0 ) i j m/s, DeerB running at ( 1 2 + 8 . 0 ) i j m/s, and DeerC running at ( 1 . 2 1 8 ) i j m/s. What is the velocity of the rock on which they were standing?

  • A ( 0 . 8 0 + 1 . 0 ) i j m/s
  • B ( 1 . 0 + 0 . 2 8 ) i j m/s
  • C ( 2 . 9 + 0 . 5 5 ) i j m/s
  • D ( 1 . 5 + 1 . 8 ) i j m/s
  • E ( 0 . 2 0 + 1 . 3 ) i j m/s