Respuesta :
Answer:
Height of the rocket be one minute after liftoff is 40.1382 km.
Explanation:
[tex]v(t)=-gt-v_e\times \ln \frac{m-rt}{m}[/tex]
v = velocity of rocket at time t
g = Acceleration due to gravity =[tex]9.8 m/s^2[/tex]
[tex]v_e[/tex] = Constant velocity relative to the rocket = 2,900m/s.
m = Initial mass of the rocket at liftoff = 29000 kg
r = Rate at which fuel is consumed = 170 kg/s
Velocity of the rocket after 1 minute of the liftoff =v
t = 1 minute = 60 seconds'
Substituting all the given values in in the given equation:
[tex]v(60)=-9.8 m/s^2\times 60 s-2,900m/s\times \ln (\frac{29,000 kg-170 kg/s\times 60 s}{2,9000 kg})[/tex]
[tex]v(60) = 668.97 m/s[/tex]
Height of the rocket = h
[tex]Velocity=\frac{Displacement}{time}[/tex]
[tex]668.97 m/s=\frac{h}{60 s}[/tex]
[tex]h=668.97 m/s\times 60 s=40,138.2 m = 40.1382 km[/tex]
Height of the rocket be one minute after liftoff is 40.1382 km.
