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Two particles A and B of masses \( 1 \mathrm{~kg} \) and \( 2 \mathrm{~kg} \) respectively are projected in the same vertical line as shown in figure with speeds \( \mathrm{u}_{\mathrm{A}}=200 \mathrm{~m} / \mathrm{s} \) and \( u_{B}=85 \mathrm{~m} / \mathrm{s} \) respectively. Initially they were \( 90 \mathrm{~m} \) apart. Find the maximum height attained by the centre of mass of the system of particles A and B, from the initial position of centre of mass of the system. Assume that none of these particles collides with the ground in that duration Take \( g=10 \mathrm{~m} / \mathrm{s}^{2} \).
(1) \( 1 \mathrm{~m} \)
(2) \( 2 m \)
(3) \( 4 m \)
(4) \( 5 \mathrm{~m} \)
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