Question

An astronaut at rest in space with mass 84 kg fires a thruster that expels 35 g of hot

gas at 875 m/s. What is the velocity of the astronaut after firing the thruster?
this is the answer but I just need to show work>>>>>>(-0.36 m/s)

Answer 1

The velocity of the astronaut is, v = - 0.36 m/s

Step-by-step explanation:

Given data,

The mass of the astronaut, M = 84 kg

The mass of the gas expelled by the thruster, m = 35 g

= 0.035 g

The velocity of the gas expelled, v = 875 m/s

According to the conservation of momentum,

MV + mv = 0

V = - mv / M

Substituting the values,

V = - 0.035 x 875 / 84

= - 0.36 m/s

The negative sign in the velocity indicates the astronaut moves opposite to the direction of velocity of gas.

Hence, the velocity of the astronaut is, v = - 0.36 m/s

Answer 2

-0.364m/s

Step-by-step explanation:

Mass of Astronaut (M₁) = 84kg

mass of gas(m₂) = 35g = 0.035kg

velocity of gas (v₂) = 875m/s

velocity of astronaut (v₁) =

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(84 * 0) + (0.035 * 0) = (84 * v₁) + (0.035 * 875)

0 = 84v₁ + 30.625

84v₁ = -30.625

v₁ = -0.364m/s