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Variation of g with Height

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Q9. An object A is dropped from rest top of a 30 m high building and at the same moment another object B is projected vertically upwards with an initial speed of 15ms^-1 from the base of the building. Mass of the object A is 2 kg while mass of the object B is 4 Kg . Find the maximum height above the ground level attained by the centre of mass of the A and B system (taking g = 10ms^-2 )

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Solution

$a c c n o f t h e c e n t e r o f m a s s a = - g i n i t i a l v e l o c i t y o f t h e c e n t e r o f m a s s u = \frac{4 * 15}{2 + 4} = 10 m / s u p w a r d . w h e n t h e v e l o c i t y o f t h e c e n t e r o f m a s s b e c o m e s z e r o i t r e a c h e s m a x i m u m h e i g h t . 0 = 10^{2} - 2 g x x = \frac{100}{20} = 5 m m a x i m u m d i s \tan c e f r o m t h e i n i t i a l p o s i t i o n i n i t i a l p o s i t i o n o f t h e s y s t e m y = \frac{30 * 2}{6} = 10 m m x i m u m h e i g h t r e a c h e d b y t h e c e n t e r o f m a s s = 10 + 5 = 15 m R e g a r d s$

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