Answer :
Final answer:
The acceleration of a 6000-kg rocket ejecting mass at 16 kg/s with a relative speed of 11 km/s, a minute after the blast, is b. 34.9 m/s².
Explanation:
The question asks what the acceleration of a rocket with an initial mass of 6000 kg is when it ejects mass at a constant rate of 16 kg/s with a constant relative speed of 11 km/s (which is converted to 11000 m/s), one minute after the blast.
To find the acceleration of the rocket a minute after the blast, we can use the following information:
- Initial mass, m0: 6000 kg
- Mass ejection rate, b: 16 kg/s
- Exhaust velocity, ve: 11000 m/s
- Time, t: 60 seconds
After one minute, the mass of the rocket will be:
m = m0 - bt = 6000 kg - 16 kg/s*60 s
m = 6000 kg - 960 kg
m = 5040 kg
The rocket's thrust (T) can be calculated by:
T = b* ve
T = 16 kg/s* 11000 m/s
T = 176000 N (Newtons)
According to Newton's second law, the acceleration (a) is:
T = m* a
So,
a = T / m
a = 176000 N / 5040 kg
a = 34.9 m/s2
The acceleration of the rocket a minute after the blast is 34.9 m/s
2, which corresponds to option b.