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Dropping Objects

A ball is pro...

Question

A ball is projected upwards from the ground with an initial speed u . The ball is at a height of 160 m twice within the time internal of 4 sec , then initial speed u is ...

Ans is 60 m/s

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Solution

Dear student,

$G i v e space s equals 160 space m a equals g equals space minus 10 space m divided by s u sin g space t h e space e q u a t i o n s s equals u t plus 1 half a t squared space w e space h a v e 160 equals u t plus 1 half cross times left parenthesis negative 10 right parenthesis t squared rightwards double arrow 160 equals u t minus 5 t squared O r 5 t squared minus u t plus 160 equals 0 S o l v i n g space t h e space q u a d r a t i c space e q u a t i o n space w e space g e t comma t equals fraction numerator space u plus square root of u squared minus left parenthesis 4 cross times 5 cross times 160 right parenthesis end root over denominator 2 cross times 5 end fraction space space space space space space space space a n d space space space space space space space space fraction numerator space u minus square root of u squared minus left parenthesis 4 cross times 5 cross times 160 right parenthesis end root over denominator 2 cross times 5 end fraction rightwards double arrow t equals fraction numerator space u plus square root of u squared minus 3200 end root over denominator 10 end fraction space space space space space space space space a n d space space space space space space space space fraction numerator space u minus square root of u squared minus 3200 end root over denominator 10 end fraction N o w space i t space i s space g i v e n space t h a t space space t i m e space i n t e r v a l space 4 space s e c space s o comma fraction numerator space u plus square root of u squared minus 3200 end root over denominator 10 end fraction space space minus space space fraction numerator space u minus square root of u squared minus 3200 end root over denominator 10 end fraction equals space 4 space space space space space space rightwards double arrow fraction numerator u plus square root of u squared minus 3200 end root minus u plus square root of u squared minus 3200 end root over denominator 10 end fraction equals 4 c a n c e l l i n g space u space a n d space w e space g e t rightwards double arrow fraction numerator 2 square root of u squared minus 3200 end root over denominator 10 end fraction equals 4 rightwards double arrow fraction numerator square root of u squared minus 3200 end root over denominator 5 end fraction equals 4 rightwards double arrow square root of u squared minus 3200 end root equals 20 O n space s q u a r i n g space b o t h space s i d e s space w e space g e t rightwards double arrow u squared minus 3200 space equals space 400 rightwards double arrow u squared equals 400 plus 3200 rightwards double arrow u squared equals 3600 rightwards double arrow u equals plus-or-minus 60 W e space i g n o r e space t h e space n e g a t i v e space s i g n space a n d space g e t u equals 60 space m divided by s R e g a r d s$

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