Worksheet: Momentum in Two Dimensions

In this worksheet, we will practice applying the principles of conservation of linear momentum and energy to situations involving two-dimensional collisions.


Three deer, DeerA, DeerB, and DeerC, all of mass 70.0 kg are standing on a flat rock of mass 2.0×10 kg that is on an ice-covered pond. A gunshot goes off and the deer scatter, with DeerA running at (15+5.0)ij m/s, DeerB running at (12+8.0)ij m/s, and DeerC running at (1.218)ij m/s. What is the velocity of the rock on which they were standing?

  • A(2.9+0.55)ij m/s
  • B(1.0+0.28)ij m/s
  • C(0.20+1.3)ij m/s
  • D(0.80+1.0)ij m/s
  • E(1.5+1.8)ij m/s


A rocket of mass 200.0 kg in deep space moves with a velocity of (121+38.0)ij m/s. Suddenly, it explodes into three pieces. The first piece has a mass of 78.0 kg and moves at (321+228)ij m/s. The second piece has a mass of 56.0 kg moves at (16.088.0)ij m/s. Find the velocity of the third piece.

  • A(216190.1)/ijms
  • B(733+79.6)/ijms
  • C(44280.0)/ijms
  • D(716130.8)/ijms
  • E(20050.6)/ijms


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.


Two billiard balls on a pool table are at rest and in contact with each other. A line 𝐿 intersects the point at which the billiard balls are in contact, where 𝐿 is tangential to the surfaces of the billiard balls at their point of contact. A cue ball travels along 𝐿 at a speed of 3.8 m/s and strikes the billiard balls simultaneously in an elastic collision. Assume that the balls’ masses are all equal to each other.

What is the speed of the cue ball after the collision?

The billiard balls have the same speed as each other after the collision. What is this speed?

After the collision, the billiard balls’ velocities are directed at angles from 𝐿, where the magnitude of the angles is the same for each ball. What is the magnitude of the angles?

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