An object has maximum range ‘X’ when projected up on the inclined plane of angle of inclination θ. The same object projected down the inclined plane has maximum range ‘Y’. If it is projected on horizontal surface with the same angle of projection range is ‘Z’ , initial velocity is same, then the relation between X,Y,Z is

Question

An object has maximum range ‘X’ when projected up on the inclined plane of angle of inclination θ. The same object projected down the inclined plane has maximum range ‘Y’. If it is projected on horizontal surface with the same angle of projection range is ‘Z’ , initial velocity is same, then the relation between X,Y,Z is

Infinity Learn · Accepted Answer

maximum range up the plane is $$R=X=Vo2g1+$$$$sin$$β  maximum range down the plane is $$R=Y=Vo2g1-$$$$sin$$β maximum range in horizontal plane is $$R=Z=Vo2g$$ consider their inversions,  $$1X=g1+$$$$sin$$β$$Vo2$$;$$1Y=g1$$−$$sin$$β$$Vo2$$;$$1Z=gVo2$$ $$2Z=1X+1Y$$ ∴$$Z=2XYX+Y$$

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