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# A jet airplane is travelling at $200 m/s$ The engine takes in $100\;m^3$ of air having mass $100 \;kg$ each second. The air is used to burn 5 kg fuel each second. The energy is used to compress the products of combustion and to eject them at the rear of the plane at $500 m/s$ relative to the plane. The thrust of the engine is

$(a)\;3.25 \times 10^4 \;N \quad (b)\;2 \times 10^4\;N \quad (c)\; 5.25 \times 10^4\;N \quad (d)\;7.25 \times 10^4 \;N$

The effective velocity of air entering the compressor is equal to the airplane velocity
$v_i=200 m/s$
Engine exhaust exerts a force to the left= (mass flow rate of fuel -air mixture) $\times$ exhaust velocity
Inlet air exerts force to right= (mass flow of inlet air) \times (inlet velocity)
Mass flow of inlet of air $=\large\frac{dmi}{dt}$
$\qquad=100 kg$
Mass flow of fuel $=\large\frac{dmj}{dt}$$=5 kg exhaust velocity =v_e=500 m/s Engine Thrust T=\bigg(\large\frac{dmi}{dt}+\frac{dmj}{dt}\bigg)$$v_e-\large\frac{dmi}{dt}$$v_i$
$\qquad =(100+5)500-100 \times 200$
$\quad\;=3.25 \times 10^4 N$
Hence a is the correct answer.

edited Feb 17, 2014 by meena.p