A boy of mass 10 kg is standing on a 4kg block as shown. The whole system is on smooth level ground. The boy jumps to the right with a velocity of 7 m/s relative to the 4 kg block. Find the maximum velocity of 1 kg block (in cm/sec) in the subsequent motion.

Engineering

Physics

Momentum and Energy Conservation for System of Particles

Question

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v_b – v₄ = –7
v_b = v₄ – 7
0 = 10(v₄ – 7) + 4v₄

$v_{4} = \frac{70}{14} = 5$

v_b = –2
at v_max a_n = 0
⇒ sp. is at N-length.

$\Rightarrow 4 \times 5 = 1 v_{1} + 4 v_{4} \Rightarrow v_{4} = \frac{20 - v_{1}}{4}$

$100 = {v_{1}}^{2} + \frac{1}{4} (400 + {v_{1}}^{2} - 40 v_{1}) \Rightarrow \frac{5 v_{1}^{2}}{4} = 10 v_{1} \Rightarrow v_{1} = 8 m / s$