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

To solve this problem, we can use the conservation of momentum principle, which states that the total momentum of a system remains constant if no external forces act on it. In this case, the system consists of the space probe and the ejected gas.

Initially, the momentum of the system is zero because the space probe is motionless. At the end of the 5-second firing of the main engine, the momentum of the system can be calculated as:

Momentum before = 0
Momentum after = (1000 kg)(20 m/s) + m(ejected gas)(-5000 m/s)

where m(ejected gas) is the mass of the ejected gas.

Setting the two momenta equal, we get:

1000 kg x 20 m/s = m(ejected gas) x (-5000 m/s)

Solving for m(ejected gas), we get:

m(ejected gas) = (1000 kg x 20 m/s) / (5000 m/s) = 4 kg

Therefore, the approximate mass of the ejected gas is 4 kg, which corresponds to choice B.

A 1000-Kg Space Probe Is Motionless in Space