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physics

mechanics

Easy

Question

$A space 30 k g space p r o j e c t i l e space m o v i n g space h o r i z o n t a l l y space w i t h space a space v e l o c i t y space v with rightwards arrow on top subscript 0 equals left parenthesis 120 m divided by s right parenthesis i with hat on top space e x p l o d e s space i n t o space t w o space f r a g m e n t s space A space a n d space B space o f space m a s s e s space 12 k g space a n d space 18 k g comma space r e s p e c t i v e l y. space T a k i n g space p o i n t space o f space e x p l o s i o n space a s space o r i g i n space a n d space k n o w l e d g e space t h a t space 3 s space l a t e r space t h e space p o s i t i o n space o f space f r a g m e n t space A space i s space left parenthesis 300 m comma space 24 m comma negative 48 m space right parenthesis comma space d e t e r m i n e space t h e space p o s i t i o n space o f space f r a g m e n t space B space a t space t h e space s a m e space i n s tan t. space$

$- 400 m, 91 m, 32 m$
$400 m, - 91 m, 32 m$
$400 m, 91 m, 32 m$
$400 m, 91 m, - 32 m$

The correct answer is: $400 m, - 91 m, 32 m$

$text Initial coordinates of end text C M equals left parenthesis 0 comma 0 comma 0 right parenthesis x text coordinates of CM after end text 3 text s, end text x subscript C M end subscript equals 120 cross times 3 equals 360 m y text coordinates of CM after end text 3 text s, end text y subscript C M end subscript equals negative 1 half g t squared equals negative 45 m text After end text 3 s open parentheses m subscript 1 plus m subscript 2 close parentheses x subscript C M end subscript equals m subscript 1 x subscript 1 plus m subscript x x subscript 2 x subscript 2 equals fraction numerator 30 cross times 360 minus 12 cross times 300 over denominator 18 end fraction equals 400 m text Similarly, end text open parentheses m subscript 1 plus m subscript 2 close parentheses y subscript C M end subscript equals m subscript 1 y subscript 1 plus m subscript 2 y subscript 2 table attributes columnalign left end attributes row cell negative 30 cross times 45 equals 12 cross times 24 plus 18 cross times y subscript 2 end cell row cell y subscript 2 equals negative 91 m end cell end table text and in end text z text coordinate, end text m subscript 1 z subscript 1 plus m subscript 2 z subscript 2 equals 0 rightwards double arrow z subscript 2 equals 32 m$

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