1. Tardigrade
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  3. Physics
  4. 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)

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Q. 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 : $(g =10\,ms^{-2})$

JEE MainJEE Main 2019Work, Energy and Power

Solution:

Time taken for the particles to collide,
$t = \frac{d}{V_{rel }} = \frac{100}{100} = 1 \sec$
Speed of wood just before collision = $gt = 10\, m/s$ & speed of bullet just before collision $v-gt$
= $100 - 10 = 90\, m/s$
Now, conservation of linear momentum just before and after the collision -
$-(0.02) (1v) + (0.02) (9v) = (0.05)v$
$\Rightarrow \, 150 \,=\, 5v$
$\Rightarrow \, v \,= \,30 \,m/s$
Max. height reached by body $h = \frac{v^2}{2g}$
$ h = \frac{30 \times 30}{2 \times 10} = 45\, m$
$\therefore $ Height above tower = $40\, m$

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