An object, with mass 83 kg and speed 15 m/s relative to an observer, explodes into two pieces, one 4 times as massive as the other; the explosion takes place in deep space. the less massive piece stops relative to the observer. how much kinetic energy is added to the system during the explosion, as measured in the observer's reference frame

On a horizontal frictionless surface, a small block with mass 0.200 kg has a collision with a block of mass 0.400 kg. immediately after the collision, the 0.200 kg block is moving at 12.0 m/s in the direction 30° north of east and the 0.400 kg block is moving at 11.2 m/s in the direction 53.1° south of east. use coordinates where the +x-axis is east and the +y-axis is north.(a) what is the total kinetic energy of the two blocks after the collision (in ) what is the x-component of the total momentum of the two blocks after the collision? (indicate the direction with the sign of your ) what is the y-component of the total momentum of the two blocks after the collision? (indicate the direction with the sign of your answer.)