# An astronaut in a space suit is motionless in outer space. The propulsion unit strapped to her back ejects some gas with a velocity of 50 m/s. The astronaut recoils with a velocity of 1.0 m/s. If the mass of the astronaut and space suit after the gas is ejected is 120 kg, the mass of the gas ejected is Option 1) 1.0 kg. Option 2) 1.9 kg. Option 3) 2.4 kg. Option 4) 3.00 kg.

As we dicussed in

Elastic Collision in 2 dimension -

$\fn_jvn \vec{P_{i}}= \vec{P_{f}}$

$\fn_jvn m_{1}v_{0}\: \: \hat{i}= \left ( m_{1}v_{1} \cos \Theta + m_{2}v_{2} \cos \beta \right )\hat{i}+\left ( m_{1}v_{1} \sin \Theta - m_{2}v_{2} \sin \beta \right )\hat{j}$

- wherein

Velocity of the gas is $50ms^{-1}$

Mass of astronaut = 120 kg

MV=mv

$m= \frac{MV}{v} = \frac{120\times1}{50} = 2.4 Kg$

Option 1)

1.0 kg.

Incorrect

Option 2)

1.9 kg.

Incorrect

Option 3)

2.4 kg.

Correct

Option 4)

3.00 kg.

Incorrect

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