First slide

Third law

Question

A rocket of mass 20kg has 180 kg of fuel. The exhaust velocity of fuel is 1.6 km/sec. Calculate the ultimate velocity of the rocket gained, when the rate of consumption of the fuel is 2kg/sec. (neglect gravity)

Moderate

A

3.7 km/sec
B

2 km/sec
C

10 km/sec
D

5 km/sec

Solution

m₀ = 20 + 180 = 200kg $m \frac{d v}{d t} = 0 + (- u_{r}) \frac{d m}{d t} \Rightarrow \int_{0}^{v} d v = - u_{r} \int_{m_{i}}^{m_{f}} \frac{1}{m} d m \Rightarrow v = u_{r} \ln \frac{m_{i}}{m_{f}}$

$\large = 1.6 \times 2.303 \times \log \left( {\frac{{200}}{{20}}} \right)$

$\large = 1.6 \times 2.303 \times \log (10)$

$\large \therefore v = 1.6 \times 2.303 = 3.68m/s$

= 3.7m/s

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