# An astronaunt at rest in space with a mass of 84kg expels 35g of hot gas at 875m/s. What is the velocity of the astronaut after firing the shot?

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### 1 Answer

Before firing,

`m_A=84 kg`

`v_A=0` m/s

`m_B` =35 g= 0.035 kg

`v_B=0` m/s

`v'_B` =875 m/s

Since the firing is instantaneous, momentum shall be conserved for the firing process. i.e.

`p_A+p_B=p'_A+p'_B`

`m_A*v_A+m_B*v_B=m'_A*v'_A+m'_B*v'_B`

Sinec `v_A` and `v_B` are both zero, the above relation reduces to,

`m'_A*v'_A+m'_B*v'_B=0`

`rArr m'_A*v'_A=-m'_B*v'_B`

`rArr v'_A=-(m'_B*v'_B)/(m'_A)`

`=-(0.035*875)/84`

`=-0.365 ` m/s

Thus, the astronaut recoils in a direction opposite to that of the moving gas with a velocity of 0.365 m/s.

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