A 1000-kg space probe is motionless in space.To start moving, its main engine is fired for 5 s during which time it ejects exhaust gases at 5000 m/s.At the end of this process it is moving at 20 m/s.The approximate mass of the ejected gas is:
A)0.8 kg
B)4 kg
C)5 kg
D)20 kg
E)25 kg

Question

A 1000-kg space probe is motionless in space.To start moving, its main engine is fired for 5 s during which time it ejects exhaust gases at 5000 m/s.At the end of this process it is moving at 20 m/s.The approximate mass of the ejected gas is: 
A)0.8 kg 
B)4 kg 
C)5 kg 
D)20 kg 
E)25 kg

Quizplus · Accepted Answer

First, we can use the conservation of momentum to find the velocity of the probe after the engine is fired:
m_probe*v_probe = m_gas*v_gas
where:
m_probe = 1000 kg (mass of the probe)
v_probe = 20 m/s (final velocity of the probe)
v_gas = 5000 m/s (velocity of the ejected gas)
Solving for m_gas, we get:
m_gas = m_probe*v_probe/v_gas - m_probe
m_gas = 1000*20/5000 - 1000
m_gas = 4 kg
Therefore, the approximate mass of the ejected gas is 4 kg, and the best choice is B.

A 1000-Kg Space Probe Is Motionless in Space