First slide

Third law

Question

A rocket has total mass 1000 kg with fuel of 900 kg. It ejects fuel at the rate of 1 kg/s with an exhaust velocity of 2 km/s relative to rocket. The maximum velocity attained by rocket is

Moderate

A

2.3 km/s
B

4.6 km/s
C

2 km/s
D

$4 .6 \log_{10} (\frac{10}{9}) km / s$

Solution

Final speed, $v_{b} = 2 .303 ulog \frac{m_{0}}{m_{c}}$
$\begin{array}{l} = 2 .303 \times 2 km / s \times \log \frac{1000}{1000 - 900} \\ = 4 .6 km / s . (\log_{10} 10 = 1) \end{array}$

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