Conservation Of Momentum

A person with mass $m_p=80$ kg stands at the stern of an iceboat of length $L=24$ m and mass $m_b=400$ kg. The boat is on smooth ice.

There are two small balls, A and B, of equal mass. Ball A collides with ball B, which is initially at rest on a smooth horizontal table. The initial velocity of ball A is $v_1 = 30$ m/s to the right. After the collision, ball A moves in a direction at an angle $\alpha = 30^\circ$ with its original direction of motion. Ball B's velocity makes an angle $\beta = 45^\circ$ with the original direction of motion of ball A.

When a rifle is fired, the bullet exits the barrel and the rifle recoils. The rifle's mass is 3 kg, and the bullet's mass is 50 g. The bullet's muzzle velocity is 600 m/s.

Two balls move towards each other, each with a speed of 2 m/s. One ball's mass is 3 times the other's. They stick together after colliding.

On a smooth horizontal surface lies a wooden block of mass 400 g. A bullet of mass 50 g hits the block with a horizontal velocity of 200 m/s. The bullet passes through the block, and its exit velocity is 160 m/s.

A grenade moving horizontally at 10 m/s explodes into two pieces with a mass ratio of 3:2. The smaller piece flies in the opposite direction at 80 m/s.

A cannon cart of mass $M$ fires a cannonball of mass $m$ at an elevation angle $\theta$. The muzzle velocity of the cannonball relative to the ground is $v_0$. The cart is initially at rest.

A shell is fired with speed $v_0$ at an elevation angle $\theta$. At the highest point of its trajectory, it explodes into two fragments of equal mass. One fragment moves upward at a 45° angle to the horizontal, and the other moves downward at a 45° angle to the horizontal.

Two people, each of mass $m$, stand on a flatcar of mass $M$ at rest. They jump off in the same horizontal direction with a velocity $v$ relative to the car.

Two blocks are in contact with a light, unattached spring between them. One block has a mass 3 times the other. The spring is compressed, storing 100 J of elastic potential energy. The blocks are released simultaneously from rest.