A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 56.6 × 105 kg, of which 8.50 × 105 kg is fuel. The rocket engine is then fired for 240 s, during which fuel is consumed at the rate of 350 kg/s. The speed of the exhaust products relative to the rocket is 2.38 km/s.
(a) What is the rocket's thrust? After the 240 s firing, what are
(b) the mass and
(c) the speed of the rocket?

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Respuesta :

shirleywashington shirleywashington · Answer 1 · 2019-09-05T09:24:02+02:00

Answer:

b) 5546000 kg

c) 48.42 m/s

Explanation:

Mass of fuel = 8.5×10⁵ kg

[tex]M_i[/tex] = Mass of ship = 56.6×10⁵ kg

R = Burn rate = 350 kg/s

[tex]v_{rel}[/tex] = Speed of the exhaust products relative to the rocket = 2.37 km/s

Thrust

[tex]T = Rv_{rel}\\\Rightarrow T = 350\times 2.38\times 10^3\\\Rightarrow T = 833000 N[/tex]

Thrust is 833000 N

Mass of fuel consumed in 240 s

350×240 = 84000 kg

Mass of ship after 240 s

[tex]M_f=M_i-\text{Mass of fuel consumed}=56.6\times 10^5-84000 = 5576000\ kg[/tex]

Mass of ship after 240 s is 5576000 kg

Speed of rocket

[tex]v=u+v_{rel}ln\frac{M_i}{M_f}\\\Rightarrow v=0+2.38\times 10^3ln\frac{56.6\times 10^5}{5576000}\\\Rightarrow v=35.58\ m/s[/tex]

The speed of the rocket after 240 s is 35.58 m/s