First slide

Second law

Question

A rocket consumes 20 kg fuel per second. The exhaust gases escape at a speed of 1000 ms^–1 relative to the rocket. Calculate the upthrust received by the rocket. Also calculate the velocity acquired. When its mass is 1/100 of the initial mass.

Moderate

Solution

$F = \frac{{m\,{v_r}}}{t} = 20 \times 1000 = 2 \times {10^4}N$
$V = {u_0} + {v_r}\,\,\log \,\,\frac{{{m_0}}}{m}$
$V = 0 + {10^3} \times 2.303\,\,\,\log \,\,\left( {\frac{{{m_0}}}{{{m_0}/100}}} \right)$
$= {10^3} \times 2.303\,\,\log (100)$
$= {10^3} \times 2.303\,\,\,\,\,\log ({10^2})$
$= {10^3} \times 2.303\,(2) = {10^3} \times 4.606\,$
V = 4.6 km / s

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