Question

3c A rocket of mass 40kg has got a fuel of mass 360 kg inside it. The exhaust velocity of the fuel is 2 km/s. The fuel is burning at the rate of 4 kg/s. Find the final velocity of rocket. 05 CO3 PO3​

Answer 1

2.419 m/s is the final velocity of rocket.

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Answer 2

Given:

• A rocket of mass 40 kg has got a fuel of mass 360 kg inside of it.
• the exhaust velocity of the fuel is 2km/s.
• the fuel is burning at the rate of 4 kg/s

To Find: The final velocity of the rocket?

using formula,

                                   $v = u - gt + v_{r}$$log\frac{m}{n}$

        ∴                        $m = 40 kg$

                                 $m_{note}$ = $200 kg$

                                 $v_{r}$ = $2$×$10^{3}$ m/s

Rate of consumption $(-\frac{dm}{dt}) =$ $4 kg/s$

                                t = 360/4 = 90 sec.

                              v = -10×40 + 2×$10^{3}$㏒$(\frac{200}{90})$

                              v = -400 + 2000㏒(2.22)

                              v = -400 + 2000×0.34

                              v = -400 + 680

                              v = 280 m/s = 0.280 km/s

hence the final velocity of rocket will be 0.280 km/s.