Ncert Exercises & Solutions

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of $4 m s^{- 1}$ relative to the trolley in a direction opposite to its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

$T h e i n i t i a l m o m e n t u m o f t h e s y s t e m (b o y + t r o l l e y)$
$= (m + M) V$
$= (200 + 20) 10 = 2200 m s^{- 1}$

$N o w a s s u m e v' i s t h e f i n a l v e l o c i t y o f t h e t r o l l e y w r t g r o u n d$
$T h e n f i n a l m o m e n t u m$
$= M v' + m (v' - 4) = 220 v' - 80$

$A p p l y i n g c o n s e r v a t i o n o f m o m e n t u m :$
$220 v' - 80 = 2200$
$o r, v' = 10.36 m s^{- 1}$

$T h e t i m e t a k e n b y t h e b o y, t$
$= \frac{10}{4} = 2.5 s$

$T h u s t h e d i s \tan c e m o v e d b y t h e t r o l l e y$
$= 10.36 \times 2.5$
$= 25.9 m$

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