A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is : (g = 10 ms

Engineering

Physics

Collision

Question

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms^–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is : (g = 10 ms^–2)

40 m

20 m

10 m

30 m

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T_cm From ground $= \frac{0 .03 \times 100}{0 .05} = 60 m$

$V_{cm} = \frac{0 .02 \times 100}{0 .05} = 40 m$

$H = \frac{V_{cm}^{2}}{2 g} = \frac{40 \times 40}{20} = 80 m$

Height above building = 80 – 40 = 40 m