It’s Newton’s First Law. If we agree (e) being <1 changes the trajectory then the cushion causes a second force to act on ball B (the first force having been caused by ball A).
I appreciate that (e) reflects physical characteristics like deformation or inelasticity that reduce kinetic energy by reducing velocity. If friction were introduced separately there would be a cumulative effect.
But it’s still fair to talk about (e) being a kind of friction when the impact...
It’s a kind of friction. The ball is hitting the cushion at an angle. As usual with vectors it’s appropriate to resolve the force of friction into two pieces, one on the y-axis and the other, which is the one we care about, on the x-axis.
You don't need to know anything about ball A beyond the fact that it was struck by the pool cue exactly as needed to send ball B from ball B's initial position to point C, point C being the exact right spot to have it end up at point D.
The x-location of Point C will vary depending on the...
On second thought, it needn't be a zero-friction environment. For example car B's driver could be applying just enough gas to keep its velocity constant.
Positive acceleration has the same direction as positive velocity, so if plus means right then minus means left. So if car A's initial negative velocity is to the left then its acceleration is to the right.
So to visualize, suppose car A is facing right--it's rolling backwards at 3.5 cm/sec when...