Question

The kinetic energy of a rocket is increased by a factor of twelve after its engines are fired, whereas its
total mass is reduced by one fifth through the burning of fuel. By what factor is the magnitude of its momentum
changed?

Answer 1

\[K = \frac{1}{2}mv^2 = \frac{p^2}{2m}\]
\[ m_f = 4m_i/5 \]
\[ p_f = np_i\]
\[12K_i = K_f\]
\[ 12 \frac{p_i^2}{2m_i} = \frac{p_f^2}{2m_f}\]
\[ 12 \frac{p_i^2}{2m_i} = \frac{5 (np_i)^2}{2(4m_i)}\]
\[ 12\frac{p_i^2}{2m_i} = \frac{5n^2}{4} \frac {p_i^2}{2m_i} \]
\[ 12 = \frac{5n^2}{4} \]
\[ n =\frac{4}{5} \sqrt{15}\]

That's the factor its momentum has increased by,.