Answer:
a) [tex]v = 312.791\,\frac{m}{s}[/tex], b) [tex]a = 13.333\,\frac{m}{s^{2}}[/tex]
Explanation:
The problem is asking the rocket velocity and acceleration at t = 6 s.
a) The general equation of the rocket is:
[tex]v=v_{o} -v_{ex}\cdot \ln \frac{m}{m_{o}}[/tex]
[tex]v = 230\,\frac{m}{s}-(1200\,\frac{m}{s} )\cdot \ln \frac{14000\,kg}{15000\,kg}[/tex]
[tex]v = 312.791\,\frac{m}{s}[/tex]
b) The acceleration experimented by the rocket is:
[tex]a = \frac{v_{ex}}{m_{o}}\cdot \frac{dm}{dt}[/tex]
[tex]a = \frac{1200\,\frac{m}{s} }{15000\,kg}\cdot \frac{1000\,kg}{6\,s}[/tex]
[tex]a = 13.333\,\frac{m}{s^{2}}[/tex]
a). The rocket's velocity of the expelled gases:
[tex]312.791 m/s[/tex]
b). The acceleration would be as follows:
[tex]13.33 m/s^2[/tex]
Given that,
Velocity of rocket = [tex]+230 m/s[/tex]
Time [tex]= 6.0 s[/tex]
Velocity of expelled gas = -1200 m/s
[tex]Fuel[/tex] [tex]= 1000 Kg[/tex]
a). Rocket's velocity
[tex]v = v_{0} - v_{ex.}[/tex] [tex].In. m/m_{o}[/tex]
[tex]= 230 m/s - (1200 m/s) . In 14000/15000[/tex]
[tex]=[/tex] [tex]312.791 m/s[/tex]
b). Acceleration
[tex]a = v_{ex}/m_{o} . dm/dt[/tex]
[tex]a = 1200/15000 . 1000/6[/tex]
∵ [tex]a =[/tex] [tex]13.33 m/s^2[/tex]
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