Question

a rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s.the acceleration of the rocket 1 minute after the blast is (g=10m/s2)
1.34.9m/s2
2.27.5m/s2
3.3.50m/s2
13.5m/s2

Answer 1

A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 minute after the blast is (g=10m/s2)

1.34.9m/s2

2.27.5m/s2

3.3.50m/s2

13.5m/s2

**Solution**

$$m = m _ {0} - \frac {d m}{d t} t \rightarrow m (1 \min ) = 5 7 0 0 - 1 5 * 6 0 = 4 8 0 0 k g.$$

For the Second Newton's law

$$m a = \frac {d m}{d t} V - m g$$ $$a = \frac {d m}{d t} * \frac {V}{m} - g = \frac {1 2 0 0 0}{4 8 0 0} * 1 5 - 1 0 = 2 7. 5 \frac {m}{s ^ {2}}$$

Right answer is 2) 27.5 $\frac{m}{s^2}$.