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t h e v e r t i c a l c o m p o n e n t o f t h e v e l o c i t y o f t h e p r o j e c t i o n i s u S i n α a n d t h e h o r i z o n t a l c o m p o n e n t i s u C o s α n o w i f t b e t h e t i m e a f t e r t h e p r o j e c t i o n o f t h e p r o j e c t i l e, i t s d i r e c t i o n o f v e l o c i t y m a k e s a n a n g l e β w i t h t h e h o r i z o n t a l . l e t t h e v e l o c i t y c o m p o n e n t o f t h e v e l o c i t y a f t e r t s e c b e v . t h e v e r t i c a l c o m p o n e n t o f t h e v e l o c i t y a f t e r t i m e t w i l l b e v S i n β b u t t h e h o r i z o n t a l c o m p o n e n t r e m a i n s u n a l t e r e d a s u C o s α s o, u C o s α = v S i n β v = \frac{u C o s α}{S i n β} = u C o s α C o s e c β

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