Applied Mechanics and Graphic Statics
The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be

sin (α - β)/sin (α + β)
tan (α - β)/tan (α + β)
cos (α - β)/cos (α + β)
sin (α + β)/sin (α - β)

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Applied Mechanics and Graphic Statics
The phenomenon of collision of two elastic bodies takes place because bodies

Attempt to regain its original shape due to their elasticities
Immediately after collision come momentarily to rest
Tend to compress each other till they are compressed maximum possible
All listed here

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