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83_Physics ProblemsTechnical Physics

83_Physics ProblemsTechnical Physics - 84 P4.8 Motion in...

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84 Motion in Two Dimensions P4.8 a j = 3 00 . ± m s 2 ; v i i = 5 00 . ± m s ; r i j i = + 0 0 ± ± (a) r r v a i j f i i t t t t = + + = + L N M O Q P 1 2 5 00 1 2 3 00 2 2 . ± . ± m v v a i j f i t t = + = + 5 00 3 00 . ± . ± e j m s (b) t = 2 00 . s , r i j i j f = + = + 5 00 2 00 1 2 3 00 2 00 10 0 6 00 2 . . ± . . ± . ± . ± a f a fa f e j m so x f = 10 0 . m , y f = 6 00 . m v i j i j v f f f xf yf v v v = + = + = = + = + = 5 00 3 00 2 00 5 00 6 00 5 00 6 00 7 81 2 2 2 2 . ± . . ± . ± . ± . . . a f e j a f a f m s m s *P4.9 (a) For the x -component of the motion we have x x v t a t f i xi x = + + 1 2 2 . 0 01 0 1 80 10 1 2 8 10 4 10 1 80 10 10 0 1 80 10 4 4 10 10 2 4 10 1 8 10 7 14 2 14 2 7 2 7 2 14 2 2 14 7 2 . . . . . m m s m s m s m s m m s 1.8 10 m s m s m m s 1.84 10 m s 8 10 m s 2 2 7 2 7 14 = + × + × × + × = = × ± × × × = × ± × × e j e j e j e j e j e je j e j t t t t t We choose the + sign to represent the physical situation t = × × = × 4 39 10 5 49 10 5 10 . . m s 8 10 m s s 14 2 . Here y y v t a t f i yi y = + + = + + × × = × 1 2 0 0 1 2 1 6 10 5 49 10 2 41 10 2 15 10 2 4 . . . m s s m 2 e je j . So, r i j f = + 10 0 0 241 . ± . ± mm e j . (b) v v a i i j i i j i j f i t = + = × + × + × × = × + × +
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