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 m`s^(-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 bulding before falling below is :
`(g=10ms^(-2))`

Options

A. 20m
B. 5m
C. 43.2 m
D. 35m

Answer

C

Explanation

`X_(cm) , i=(0.3 xx 20)/(0.5) = 12m `
` V_(cm), i=(0.2 xx 80)/(0.5) = 32m//s`
` H_(max)` of centre of mass
above `P = (32 xx 32)/(2 xx 10) = 51.2 m`
Height above top of building = 51.2 - 8 = 43.2 m