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Velocity of COM

Two balls of ...

Question

Two balls of equal masses are projected upward simultaneously, one from the ground with speed $50 m / s$ and other from a $40 m$ high tower with initial speed $30 m / s$ . Find the maximum height attained by their centre of mass.

100 m

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200 m

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150 m

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50 m

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Solution

The correct option is A 100 m
$V_{C M} = \frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}} = (v_{1} + v_{2}) / 2$
$I n i t i a l l y, U_{C M} = 40 m / s X_{C M} = 40 / 2 = 20 m a b o v e g r o u n d . M a x i m u m h e i g h t m e a n s V_{C M} = 0 T h a t i s, 0^{2} - 40^{2} = 2 \times (- 10) \times (H - 20) T h u s H = 100 m$

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A

B

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50 {ms}^{- 1}

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