When the 5 kg velocity vector was (4 m/s, 330 degrees), a reference frame rotation of degrees would transform the 2-dim collision to the horizontal direction as a 1-dim collision. In daily life a tree is non-moving according to a sidewalk pedestrian observer at rest. But the same tree would appear to move toward the right at ( + 7 m/s) according to an observer inside a car moving (- 7 m/s) toward the l.

The car observer measured initial energy as 0.5*5*6*6 Joules = 90 J and final energy as 0.5*5*(-3)*(-3) + 0.5*30*(+1.5)*(+1.5) Joules = 56.25J with a loss of Joules. The sidewalk pedestrian observer reported an initial energy of 0.5*5*(+4)*(+4) + 0.5*30*(-2)*(-2) = 100 J and final energy as 0.5*5*(-5)*(-5) + 0.5*30*(-0.5)*(-0.5) = 66.25J with a loss of Joules. The arithmetic showed that the total kinetic energy loss to heat, sound, etc. of the two-object system (impactor-target system) is the s for both observers, just like the exchange impulse of 45 N-sec is the s for both observers.

The observed energy gain of a smaller mass object in a collision, the slingshot effect, could be an energy loss of that smaller mass in another reference f , due to the requirement of relative velocity such that kinetic energy is a r concept while the total kinetic energy loss to heat, sound, etc. of the two-object system (impactor-target system) must be an invariant for both observers. The s principle helps to design gravity assisted rocket launch of spacecraft missions for the exploration of the outer planets.

In the above Whiteboard example, after the collision the 30 kg was observed moving toward the right (+1.5 m/s) for an observer moving at (-2 m/s) toward the left such that the 30 kg was moving at (-0.5 m/s) toward the l___ for the sidewalk pedestrian observer. The sidewalk pedestrian observer would draw a conclusion that the 30 kg with initial (-2m/s) had slowed down to (-0.5 m/s) and lost energy during the collision, with an apparent contradiction to the car-observer seeing the 30 kg at rest before the collision to become moving at +1.5 m/s and gaining kinetic energy. The apparent contradiction is removed using the concept of relative v.

The nylon net would extend the contact time during the impact such that the contact force would be s when the impulse must be equal to the change of the m of the egg in a collision

The center of mass must remain at the same v with no external force, regardless of the internal collisions.