Answer :
Answer:
a) [tex]v \approx 834.278\,\frac{m}{s}[/tex], b) [tex]a = 96.667\,\frac{m}{s^{2}}[/tex]
Explanation:
a) The maximum speed of the rocket is given by the Tsiolkovski's Equation:
[tex]v =v_{o} - v_{ext}\cdot \ln \left(\frac{m}{m_{o}} \right)[/tex]
[tex]v = 0\,\frac{m}{s} - (2900\,\frac{m}{s} )\cdot \ln \left(\frac{450\,kg}{600\,kg} \right)[/tex]
[tex]v \approx 834.278\,\frac{m}{s}[/tex]
b) The acceleration is obtained by deriving the Tsiolkolski's Equation:
[tex]a = -v_{ext}\cdot \left(\frac{1}{m}\left) \cdot \dot m[/tex]
The maximum acceleration occured when fuel is entirely consumed. Then:
[tex]a = - \left(2900\,\frac{m}{s} \right)\cdot \left(\frac{1}{450\,kg} \right)\cdot \left(-15\,\frac{kg}{s} \right)[/tex]
[tex]a = 96.667\,\frac{m}{s^{2}}[/tex]