A mass of 2 kg is thrown up with a velocity of $50 \mathrm{~m} / \mathrm{s}$. After 3 seconds, it ex

Question

A mass of 2 kg is thrown up with a velocity of $50 \mathrm{~m} / \mathrm{s}$. After 3 seconds, it explodes into two parts. One part of mass 800 g comes down with a velocity of $10 \mathrm{~m} / \mathrm{s}$. The velocity of the other part is (Take $g=10 \mathrm{~m} \mathrm{s}^{-2}$)

Professor PC Thomas Classes · Answer

Velocity after 3s is $v = u - gt = 50 - 10 	imes 3 = 20 \mathrm{~m/s}$ (upwards). Total momentum $p = M v = 2 	imes 20 = 40 \mathrm{~kg~m/s}$. After explosion: $m_1 = 0.8 \mathrm{~kg}, v_1 = -10 \mathrm{~m/s}$, $m_2 = 1.2 \mathrm{~kg}, v_2 = ?$. By conservation of momentum: $40 = 0.8(-10) + 1.2(v_2) \implies 40 = -8 + 1.2 v_2 \implies 48 = 1.2 v_2 \implies v_2 = 40 \mathrm{~m/s}$ (upwards).