A body has maximum range R_(1) when projected up the inclined plane. The same body when projected down the inclined plane, it has maximum range R_(2). Find its maximum horizontal inclined plane inte line of the greates slope.

A body has maximum range R_(1) when projected up the inclined plane. T

1.	A body has maximum range R_(1) when projected up the inclined plane. The same body when projected down the inclined plane, it has maximum range R_(2). Find its maximum horizontal inclined plane inte line of the greates slope.
Answer» Solution :For upward projection `R_("MAX")=(v_(0)^(2))/(g(1+SIN beta))=R_(1)`………..i For downward projection `R_("max")=(v_(0)^(2))/(g(1-sin beta))=R_(2)`………ii For a projection on horizontal SURFACE substituting `beta=0` Then We have `R_("max")=(v_(0)^(2))/g=R` (say) ...........iii To establish a relation between `R,R_(1)` and `R_(2)`we need to eliminate `sin beta`. Adding `1/(R_(1))` from eq (i) with `1/(R_(2)0` from eq (ii) we have `2/R=1/(R_(1))+1/(R_(2))` Then `R=(2R_(1)R_(2))/(R_(1)+R_(2))`