**Variant 1**

1. A body moves in a straight line having an initial momentum of 70 kg-m/s. For a time of 4.5 s some force acts on the body, as a result of which the momentum reaches the value of 160 kg-m/s. Determine the force acting on the body (the direction of the force coincides with the direction of the initial velocity of the body).

2. A recoilless gun is mounted on a stationary railroad platform weighing 25 tons and fired along the rails at an angle of 60° to the horizon. The mass of the projectile is 40 kg. The velocity of the platform after the shot is 1.2 m/s. Determine the velocity of the projectile when fired.

3. A boat 3 m long is standing on calm water. A fisherman weighing 70kg moves from the bow of the boat to the stern, and the boat shifts 0.9m relative to the shore. What is the mass of the boat?

4. A steel ball of mass 0.05 kg falls from a height of 5 m onto a steel plate. After the collision the ball bounces off the plate with the same modulo velocity. Find the force acting on the slab during the impact, considering it constant. The time of impact is 0.01 s.

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**Body momentum. Law of conservation of momentum**

**Variant 2**

1. A body moves in a straight line having an initial momentum of 45 kg-m/s. For time t a force equal to 30N acts on the body, as a result of which the momentum reaches the value of 90 kg-m/s. Determine the time interval. (The direction of the force coincides with the direction of the body’s initial velocity.)

2. A stationary railroad platform weighing 20t is mounted on a recoilless gun, from which a shot is fired along the rails at an angle of 30° to the horizon. The velocity of the platform after the shot is 2.1 m/s. Determine the mass of the projectile if the velocity of the projectile when fired is 1.4 km/sec.

3. The boat is 2.8 m long and weighs 170 kg standing on calm water. The fisherman moves from the bow of the boat to the stern, the boat shifts 0.9 m relative to the shore. Determine the mass of the fisherman.

4. During maneuvers at a railway station two platforms with masses m1 = 2.4*104 kg and m2 = 1.6*104 kg moved toward each other with speeds whose moduli are equal to v1 = 0.5 m/s and v2 = 1 m/s. Find the velocity of their joint motion after the coupling has worked?

**The momentum of the body. The law of conservation of momentum.**

**Option 3**

1. A force equal to 20N acts on a body moving in a straight line for 6.5s, as a result of which the momentum reaches the value of 150 kg-m/s. Determine the initial momentum of the body. The direction of the force coincides with the direction of the initial velocity of the body.

2. A recoilless gun is mounted on a stationary railroad platform and is fired along the rails at an angle of 30° to the horizon. The mass of the projectile is 40 kg, and its velocity at the shot is 1.5 km/s. The velocity of the platform after the shot is 1.2 m/s. Determine the mass of the platform.

3. A boat 3.4 m long and weighing 160 kg stands on calm water. A fisherman weighing 50kg moves from the bow of the boat to the stern. Determine the distance by which the boat will shift relative to the shore.

4. Two plasticine balls, the ratio of their masses m2/m1 =4, after their collision have stuck together and started moving along a smooth horizontal surface with speed U. Determine the velocity of the light ball before the collision if it moved three times faster than the heavy ball (V1=3V2), and the directions of motion of the balls were mutually perpendicular. Neglect friction.

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**Body momentum. The law of conservation of momentum**

**Variant 4**

1. A body moves in a straight line having an initial momentum of 30 kg-m/s. For a time of 3.5 s a force equal to 80N acts on the body. Determine the momentum that the body will gain as a result of the force. (The direction of the force coincides with the direction of the initial velocity of the body).

2. On a stationary railroad platform, weighing 25 tons, a recoilless gun is mounted, which is fired along the rails at an angle of 60° to the horizon. The mass of the projectile is 40 kg, and its velocity at firing is 1.2 km/s. Determine the velocity of the platform after the shot.

3. A boat with a mass of 150kg on calm water. A fisherman weighing 50kg moves from the bow of the boat to the stern, and the boat shifts 0.8m relative to the shore. Determine the length of the boat.

4. A grasshopper sits on the end of a straw of length l, which lies on a smooth floor. The grasshopper jumps and gets on the other end of the straw. With what minimum initial velocity with respect to the ground Vmin should it jump, if its mass is M and the mass of the straw is m? Do not consider air resistance and friction.

**Body momentum. Law of conservation of momentum**

**Variant 5**

1. A body moves in a straight line having an initial momentum of 105 kg-m/s. Some force acts on the body for a time of 0.5 s, as a result of which the momentum reaches the value of 120 kg-m/s. Determine the force acting on the body (the direction of the force coincides with the direction of the initial velocity of the body).

2. A recoilless gun is mounted on a stationary railroad platform weighing 20 tons and fired along the rails at an angle of 30° to the horizon. The mass of the projectile is 30 kg. The velocity of the platform after the shot is 1.8 m/s. Determine the velocity of the projectile when fired.

3. A boat 3.2 m long is standing on calm water. A fisherman weighing 80kg moves from the bow of the boat to the stern, and the boat shifts 1.2m relative to the shore. What is the mass of the boat?

4. At the initial moment the rocket of mass M had velocity V0. At the end of each second a portion of gas of mass m is ejected from the rocket. The velocity of the gas portion differs from the velocity of the rocket before the combustion of a given mass of gas by a constant value equal to u, i.e., the rate of gas flow is constant. Determine the velocity of the rocket after n seconds. Do not consider the action of gravity.

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**Body momentum. The law of conservation of momentum**

**Variant 6**

1. A body moves in a straight line having an initial momentum of 50 kg-m/s. For time t a force equal to 10N acts on the body, as a result of which the momentum reaches the value of 95 kg-m/s. Determine the time interval. (The direction of the force coincides with the direction of the body’s initial velocity.)

2. A stationary railroad platform weighing 25 tons has a recoilless gun mounted on it, from which a shot is fired along the rails at an angle of 60° to the horizon. The velocity of the platform after the shot is 0.7 m/s. Determine the mass of the projectile if the velocity of the projectile when fired is 1.3 km/sec.

3. A boat 3 m long and weighing 160 kg stands on calm water. The fisherman moves from the bow of the boat to the stern, the boat shifts 0.95 m relative to the shore. Determine the mass of the fisherman.

4. Hot gases fly out of a rocket with velocity 2000 m/s relative to the hull. What is the force of the rocket’s thrust if every second 100 kg of gases are released from the rocket?

**The momentum of the body. The law of conservation of momentum**

**Option 7**

1. A force of 40N acts on a body moving in a straight line for 7.5s, as a result of which momentum reaches a value of 325 kg-m/s. Determine the initial momentum of the body. The direction of the force coincides with the direction of the initial velocity of the body.

2. A recoilless gun is mounted on a stationary railroad platform and is fired along the rails at an angle of 60° to the horizon. The mass of the projectile is 30 kg, and its velocity at the shot is 1.4 km/s. The velocity of the platform after the shot is 0.7 m/s. Determine the mass of the platform.

3. A boat with a length of 3.1 m and a mass of 180 kg stands on calm water. A fisherman weighing 60kg moves from the bow of the boat to the stern. Determine the distance by which the boat will shift relative to the shore.

4. After its explosion a grenade, rotating horizontally at speed of 10 m/s, has split into two shards of masses 1 kg and 1.5 kg. The velocity of the large fragment has increased to 25 m/s and it continued moving in a horizontal direction. Find the velocity and direction of motion of the smaller fragment.

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**Body momentum. Law of conservation of momentum**

**Option 8.**

1. A body moves in a straight line having an initial momentum of 85 kg-m/s. For a time of 5 s a force equal to 15N acts on the body. Determine the momentum that the body will gain as a result of the force. (The direction of the force coincides with the direction of the initial velocity of the body).

2. A stationary railroad platform weighing 25 tons has a recoilless gun, which is fired along the rails at an angle of 30° to the horizon. The velocity of the platform after the shot is 1.8 m/s. Determine the mass of the projectile if the velocity of the projectile when fired is 1.2 km/sec.

3. A boat with a mass of 200kg on calm water. A fisherman weighing 70 kg moves from the bow of the boat to the stern, the boat shifts by a distance of 1.1 m relative to the shore. Determine the length of the boat.

4. Two inelastic balls with masses of 6 kg and 4 kg move with velocities of 8 m/s and 3 m/s, directed along one straight line. How will their velocity change after a totally inelastic collision if the first ball catches up with the second.

**The momentum of the body. Law of conservation of momentum**

**Variant 9**

1. A body moves in a straight line having an initial momentum of 75 kg-m/s. Some force acts on the body for 1.5 s, as a result of which the momentum reaches the value of 105 kg-m/s. Determine the force acting on the body (the direction of the force coincides with the direction of the initial velocity of the body).

2. A recoilless gun is mounted on a stationary railroad platform weighing 20 tons and fired along the rails at an angle of 30° to the horizon. The mass of the projectile is 40 kg. The velocity of the platform after the shot is 1.7 m/s. Determine the velocity of the projectile when fired.

3. A boat 3.5 m long is standing on calm water. A 90kg fisherman moves from the bow of the boat to the stern, and the boat shifts 0.85m relative to the shore. What is the mass of the boat?

4. A platform with a mass of 50 kg, moving on rails at a speed of 0.2 m/s, has 200 kg of coal added on top. Calculate by how much the velocity of the platform decreased.

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**Body momentum. Law of conservation of momentum**

**Variation 10**

1. A body moves in a straight line having an initial momentum of 50 kg-m/s. For time t a force equal to 50N acts on the body, as a result of which the momentum reaches the value of 175 kg-m/s. Determine the time interval. (The direction of the force coincides with the direction of the body’s initial velocity.)

2. A recoilless gun is mounted on a stationary railroad platform weighing 25 tons and fired along the rails at an angle of 60° to the horizon. The mass of the projectile is 40 kg, and its velocity at firing is 1.3 km/s. Determine the speed of the platform after the shot.

3. A boat with a length of 3.3 m and a mass of 190 kg stands on calm water. The fisherman moves from the bow of the boat to the stern, and the boat shifts 1.0 m relative to the shore. Determine the mass of the fisherman.

4. A cannon has a mass of 800 kg. The mass of the shot is 10 kg. The shot leaves with an initial velocity of 200 m/s and moves relative to the Earth at an angle of 60®. What is the recoil velocity of the cannon? Neglect friction.