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Dear Student,

l e t u b e t h e h o r i z o n t a l v e l o c i t y g i v e n t o t h e p a r t i c l e o f m a s s m . R b e t h e h o r i z o n t a l r a n g e . T i l l r e a c h i n g t o t h e h i g h e s t p o i n t, h o r i z o n t a l d i s \tan c e t a r v e l l e d i s g i v e n i s R / 2 A t t h e h i g h e s t p o i n t, i t g e t s b r e a k i n t o t w o p a r t s, e a c h o f m a s s m / 2 . a c c o r d i n g t o t h e l a w o f c o n s e r v a t i o n o f m o m e n t u m m u = \frac{m u 1}{2} - \frac{m u 2}{2} u 1 = 2 u + u 2 b o t h h a v e d i f f e r e n t d i r e c t i o n p a r t i c l e m o v i n g w i t h v e l o c i t y u 2 r e a c h e d t o t h e i n i t i a l p o s i t i o n . h o r i z o n t a l d i s \tan c e t a r v e l l e d b y t h i s p a r t i c l e i n t i m e t i s g i v e n b y : \frac{R}{2} = u 2 t u 2 = \frac{R}{2 t} d i s \tan c e t r a v e l l e d b y p a r t i c l e m o v i n g w i t h v e l o c i t y u 1 i s g i v e n b y; x = (2 u + u 2) t x = 2 u t + u_{2} t x = \frac{2 u T}{2} + u 2 t x = R + \frac{R}{2} x = \frac{3 R}{2} r a n g e i s g i v e n b y = i n i t i a l h o r i z o n t a l d i s \tan c e t a r v e l l e d b b e f o r e b r e a k i n g + x r a n g e = \frac{3 R}{2} + \frac{R}{2} = 2 R

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