First slide

Second law

Question

In a rocket the mass of the fuel is 90% of the total mass. The rocket is blasted from the launching pad. If the exhaust gases are ejected at a rate of $500 {ms}^{- 1}$ what is the maximum speed attained by the rocket ? Neglect the effects of gravity and air resistance.

Moderate

A

$1 .15 {kms}^{- 1}$
B

$1 {kms}^{- 1}$
C

$1 .5 {kms}^{- 1}$
D

$9 {kms}^{- 1}$

Solution

Maximum speed attained $= V_{max} = Vln \frac{M_{0}}{M_{c}}$
As mass of the fuel is 90% of the total mass
$\begin{array}{l} = 500 \times 2 .303 \log_{10} 10 = 1 .15 {kms}^{- 1} \\ ∵ M_{c} = mass of the container \\ = M_{\circ} - \frac{90}{100} M_{\circ} \\ = \frac{10}{100} M_{\circ} \\ \Rightarrow \frac{M_{\circ}}{M_{c}} = 10 \end{array}$

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