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Worksheet: Conservation of Linear Momentum


A paving truck with a mass of 5 . 0 × 1 0 3 kg drives in a straight line at 2.5 m/s and dumps 1 . 0 × 1 0 3 kg of gravel on the road, taking negligible time. What is the speed of the truck after dumping the gravel?


Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 1 . 5 0 × 1 0 5 kg and a velocity of ( 0 . 3 0 / ) m s i , and the second having a mass of 1 . 1 0 × 1 0 5 kg and a velocity of ( 0 . 1 2 / ) m s i . What is their final velocity?


A child of mass 32 kg is coasting at 2.4 m/s over flat ground in a wagon of mass 7.6 kg. The child drops a ball of mass 0.83 kg out of the back of the wagon. What is the speed of the wagon after the ball is dropped?


A figure skater whose mass is 75 kg moves at 6.2 m/s towards his 50-kg-mass partner. The skater’s partner is moving at 5.5 m/s, in the same direction as the skater. When the skater catches up with his partner, he picks her up, without exerting any horizontal forces on his skates. What speed does the skater move at while he is lifting his partner?


An elephant of mass 2 1 2 5 kg is chasing a hunter of mass 76.5 kg. The elephant is moving at a speed of 6.33 m/s while the hunter is moving at a speed of 8.12 m/s. Both the elephant and the hunter are moving in the same direction, which corresponds to positive displacement.

What is the momentum of the elephant?

What is the momentum of the hunter?

The hunter stops moving and fires a tranquilizer dart of mass 275 g at the elephant. The dart moves at 650 m/s. What is the dart’s momentum?


A family is skating. The father has a mass of 68 kg, the mother 76 kg, and the daughter 34 kg. The father skates at 8.2 m/s in the positive 𝑥 -direction and collides with the mother, who is moving at 2.4 m/s at an angle 3 3 below the negative 𝑥 -direction. The two of them stick together after colliding. The pair then collide with their stationary daughter, and the three of them stick together.

What speed does the family move at?

At what angle below the positive 𝑥 -axis is the motion of the family after the collision?


An initially stationary football player of mass 90 kg catches a football of mass 0.50 kg that is thrown to him with a horizontal speed of 17 m/s and negligible vertical speed. What is the horizontal speed of the football player after catching the ball?


A man of mass 62 kg stands at rest on an icy surface that has negligible friction. He throws a ball of mass 670 g, giving the ball a horizontal velocity of 8.2 m/s. What horizontal velocity does the man have after throwing the ball?


A boy of mass 45 kg is in a sled of mass 8.2 kg. The sled slides across a frictionless ice-covered lake at 8.4 kg. There is a boulder with a mass of 670 kg in the middle of the lake. The sled crashes into the boulder, propelling the boy over it, where the boy continues sliding over the ice at 8.4 m/s.

What is the speed of the sled after the collision?

What is the speed of the boulder after the collision?


A superball is a ball that rebounds from surfaces that it collides with in such a way that it dissipates no energy. A superball of mass 0.25 kg is dropped from a vertically upward displacement of 1.5 m above a horizontal surface, hits the surface, and bounces vertically upward to the point from which it was dropped.

What was the change of momentum of the superball due to its collision with the surface?

What was the change of momentum of Earth due to its collision with the superball?

Find the change in Earth’s speed due to its collision with the superball. Use a value of 5 . 9 7 × 1 0 2 4 kg for the mass of Earth.

  • A 4 . 7 × 1 0 1 5 m/s
  • B 4.7 m/s
  • C 4 . 7 × 1 0 2 5 m/s
  • D 4 . 7 × 1 0 5 m/s
  • E 4 . 7 × 1 0 1 2 m/s


Three skydivers are falling vertically downward. The skydivers initially held on to each other and then pushed apart. Two skydivers of masses 63 kg and 84 kg gain horizontal velocities of 1.5 m/s north and 1.9 m/s southeast respectively. The third skydiver has a mass of 58 kg.

What is the horizontal speed of the third skydiver?

At what angle west of south is the motion of the third skydiver?


Two cars of equal masses approach a frictionless perpendicular intersection. Car A travels north at 22 m/s and car B travels east. The cars collide and stick together, traveling at 1 7 north of east. What was the initial speed of car B?


A railroad freight car of mass 2 2 5 0 kg travels at 3.5 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 2.0 m/s, what is the maximum mass of grain that can be dumped into the freight car?


A proton collides with a neutron and they bond to form a deuteron, as shown in the diagram. Before the collision, the proton was moving to the right at a speed of 7 . 0 × 1 0 6 m/s and the neutron was moving to the left at a speed of 4 . 0 × 1 0 6 m/s. Find the velocity at which the deuteron moves, assuming that displacement to the right corresponds to positive values. Use a value of 1 . 6 7 × 1 0 2 7 kg for the masses of both the proton and the neutron. Assume that the proton and the neutron interact classically; ignore any effects of special relativity or quantum mechanics.