Q

# I need help with 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 s

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.

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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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