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Confused! kindly explain, A 30.0kg mass falls from a height of 4.0m. The momentum of the mass just before it hits the ground is

A 30.0 kg mass falls from a height of 4.0 m. The momentum of the mass just before it hits the ground  is

  • Option 1)

    144.2 kg m/s

  • Option 2)

    187.8 kg m/s.

  • Option 3)

    320.0 kg m/s.

  • Option 4)

    442.4 kg m/s.

 
Answers (1)
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As discussed in

Perfectly Elastic Collision -

Law of conservation of momentum and that of Kinetic Energy hold good.

- wherein

\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}= \frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}

m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}

m_{1},m_{2}:masses

u_{1},v_{1}:initial \: and\: final \: velocity\: of \: the\: mass\ m_{1}

u_{2},v_{2}:initial \: and\: final \: velocity\: of \: the\: mass\ m_{2}

 

 P=mv

v^{2}= u^{2}+2gh        u=0

v = \sqrt{2gh}\Rightarrow P = m\sqrt{2gh}

v= \sqrt{2\times 10\times 4} = 8.944 \:\: ms^{-1}

P=30\times 8.944=268.32 \:\: kg \:\: ms^{-1}


Option 1)

144.2 kg m/s

This solution is incorrect

Option 2)

187.8 kg m/s.

This solution is incorrect

Option 3)

320.0 kg m/s.

This solution is incorrect

Option 4)

442.4 kg m/s.

This solution is incorrect

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