# Conservation of momentum in two dimensions

##### Intros
###### Lessons
1. Introduction to conservation of momentum in two dimensions

• Review of conservation of momentum
• Vector nature of momentum and conservation of momentum
##### Examples
###### Lessons
1. $\bold{\sum\vec{p}_i = \sum\vec{p}_f}:$ Objects that bounce apart after collision in two dimensions
1. 1.25 kg ball A is moving at 3.40 m/s [E] when it strikes stationary 1.00 kg ball B. After the collision, ball A moves off at an angle of [60.0° N of E], and ball B moves off at an angle of [30.0° S of E]. Find the velocities of A and B after collision.
2. 1.10 kg puck A travelling at 2.00 m/s [E] collides with 0.860 kg puck B moving 0.400 m/s [W]. After the collision, puck A moves off at 1.60 m/s [40.0° N of E]. Find the velocity of puck B.
2. $\bold{\sum\vec{p}_i = \sum\vec{p}_f}:$ Objects that stick together after collision in two dimensions
1. 1100.0 kg car A travelling at 12.0 m/s [E] collides with 975 kg car B travelling 19.0 m/s [N]. The cars stick together. Find the velocity of the two vehicles after collision.
2. 0.50 kg magnetic puck A travelling at 1.1 m/s collides with 0.35 kg puck B travelling with an unknown velocity, as shown in the diagram. The two pucks stick together and travel due [E]. Find the initial velocity of the second puck.
3. $\bold{\sum\vec{p}_i = \sum\vec{p}_f}:$ Objects that explode apart in two dimensions
1. A bomb initially at rest explodes, sending three fragments in different directions as shown in the diagram. Find the velocity of the 0.71 kg fragment.
2. A 21.0 kg child holding a 0.755 kg snowball rides a 3.00 kg sled on a frictionless ice surface at 2.50 m/s [E]. The child throws the snowball, giving it an impulse due [N] relative to the sled. The snowball travels at 6.00 m/s immediately after it is thrown.

3. Balls A, B, and C roll together as shown in the diagram, with all three balls colliding at the same time. Find the mass of ball C if the 3 balls are stationary after colliding.
4. A spacecraft with a total mass of 8620 kg is travelling through space at a speed of 156 m/s. Control wants to adjust its direction by 25.0°, and increase its speed to 175 m/s. Gas is ejected though a thruster on the side of the craft, travelling at 85.0° clockwise from the craft's original direction of motion. Find the mass of gas ejected.