Worksheet: Conservation of Linear Momentum

In this worksheet, we will practice applying the conservation of linear momentum to situations involving exchanges of momentum between objects.


A paving truck with a mass of 5.0×10 kg drives in a straight line at 2.5 m/s and dumps 1.0×10 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 1.50×10 kg and a velocity of (0.30/)msi, and the second having a mass of 1.10×10 kg and a velocity of (0.12/)msi. What is their final velocity?

  • A ( 0 . 2 2 / ) m s i
  • B ( 0 . 1 2 / ) m s i
  • C ( 0 . 3 6 / ) m s i
  • D ( 0 . 2 2 / ) m s i
  • E ( 0 . 1 2 / ) m s i


A figure skater whose mass is 75 kg moves at 6.2 m/s toward 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?


A cyclist of mass 60.0 kg sits on a bicycle of mass 10.0 kg, moving at 15 m/s in the positive 𝑥-direction. A bug of mass 5.0 g splatters on her cycle helmet. The bug was initially moving at 2.0 m/s in the same direction as the cyclist.

What is the combined momentum of cycle and cyclist before colliding with the bug?

  • A 3 . 1 × 1 0 i kg⋅m/s
  • B 2 . 6 × 1 0 i kg⋅m/s
  • C 1 . 9 × 1 0 i kg⋅m/s
  • D 1 . 1 × 1 0 i kg⋅m/s
  • E 0 . 6 5 × 1 0 i kg⋅m/s

What is the initial momentum of the bug?

  • A 0 . 0 1 0 i kg⋅m/s
  • B 0 . 0 0 7 2 i kg⋅m/s
  • C 0 . 0 1 6 i kg⋅m/s
  • D 0 . 0 2 0 i kg⋅m/s
  • E 0 . 0 1 2 i kg⋅m/s

What is the change in the cyclist’s velocity due to colliding with the bug?

  • A 0 . 1 1 i mm/s
  • B 0 . 9 3 i mm/s
  • C 0 . 7 3 i mm/s
  • D 0 . 9 1 i mm/s
  • E 0 . 8 0 i mm/s

If the bug had been moving in the opposite direction to the cyclist, how much of a velocity change would have resulted from the collision?

  • A 1 . 2 i mm/s
  • B 1 . 8 i mm/s
  • C 6 . 6 i mm/s
  • D 8 . 3 i mm/s
  • E 1 . 6 i mm/s


A squid of mass 5.00 kg that is initially at rest ejects 0.250 kg of fluid with a velocity of 10.0 m/s. The squid moves in the direction opposite to the direction of the ejected fluid. A frictional force of 5.00 N opposes the squid’s movement.

What is the recoil velocity of the squid if the ejection is done in 0.100 s?

How much energy is lost to work done against friction?


A 35 kg child sleds down a hill and then coasts along the flat section at the bottom, where a second 35 kg child jumps on the sled as it passes by her. If the speed of the sled is 3.5 m/s before the second child jumps on, what is its speed after she jumps on?


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 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?


An elephant of mass 2,125 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 33 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?


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?


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 17 north of east. What was the initial speed of car B?


A railroad freight car of mass 2,250 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?


An astronaut of mass 91 kg is separated from his spaceship by a distance of 7.4 m and is moving directly away from it at 0.16 m/s. To get back to the spaceship, the astronaut throws a tool bag of mass 8.2 kg directly away from the spaceship at a speed of 6.3 m/s. How much time passes before the astronaut regains contact with the spaceship?


Grain from a hopper falls onto the left end of a horizontal conveyor belt that is 2 m long. The grain falls onto the conveyor belt at a rate of 10 kg/s, the grain has no horizontal velocity when it lands on the conveyor belt. The conveyer belt transports the grain along its length at a constant speed of 2 m/s before dropping the grain off at the belt’s right end.

What force is needed to keep the conveyor belt moving at its constant speed?

What is the minimum power of the motor driving the conveyor belt?


A firecracker of mass 130 g is launched vertically upward and explodes into two pieces at its point of maximum upward vertical displacement. After the explosion, a piece of the firecracker with a mass of 58 g moves west at 14 m/s.

At what speed does the other piece of the firecracker move?

At what angle from east does the other piece of the firecracker move?


A load of gravel is dumped vertically downward into a freight car of mass 20,500 kg that is moving horizontally at 3.0 m/s on a straight section of a railroad. The freight car’s speed after receiving the load of gravel is 1.8 m/s. What is the mass of the load of gravel?


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 5.97×10 kg for the mass of Earth.

  • A 4 . 7 × 1 0 m/s
  • B4.7 m/s
  • C 4 . 7 × 1 0 m/s
  • D 4 . 7 × 1 0 m/s
  • E 4 . 7 × 1 0 m/s


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 7.0×10 m/s and the neutron was moving to the left at a speed of 4.0×10 m/s. Find the velocity at which the deuteron moves, assuming that displacement to the right corresponds to positive values. Use a value of 1.67×10 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.

  • A 1 . 5 × 1 0 i m/s
  • B 7 . 5 × 1 0 i m/s
  • C 1 . 5 × 1 0 i m/s
  • D 3 . 0 × 1 0 i m/s
  • E 3 . 0 × 1 0 i m/s


A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg that is traveling north at 40 km/h, as shown in the diagram. After the two vehicles collide, they lock together.

Find the speed of the vehicles after the collision.

At what angle east of north do the vehicles move after the collision?


Two hockey pucks, one red and one blue, each of mass 15 g, are on a flat, horizontal ice hockey rink surface that produces negligible frictional resistance to the motion of the pucks. The red puck is initially at rest and the blue puck is initially moving at a speed of 2.5 m/s to the left, as shown in the diagram. The blue puck collides with the red puck. After the collision, the red puck is moving to the left at a speed of 2.5 m/s. Find the velocity of the blue puck after the collision. Assume that displacement to the right corresponds to positive values.


A scuba tank is a cylinder that has a mass of 14.4 kg when empty and is filled with compressed air of negligible mass. While at rest, at an instant 𝑡, the tank suddenly ruptures and the escaping compressed air breaks the tank into three separate pieces, piece A, piece B, and piece C, each of which moves independently, as shown in the diagram. At the instant 𝑡, piece A has a mass of 4.5 kg and an instantaneous speed of 105 m/s in the positive 𝑥-direction while piece B has a mass of 3.2 kg and an instantaneous speed of 77 m/s in a direction 19 above the positive 𝑥-direction.

What instantaneous speed does piece C have at the instant 𝑡? Give your answer to three significant figures.

At what angle below the negative 𝑥-direction is the motion of piece C directed at the instant 𝑡? Give your answer to two significant figures.

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