I tried much to solve this question but couldn't get answer.
Q. A jet engine consumes 1 kg of fuel for each 40 kg of air intake. Fuel consumption is 1 kg/sec. When aircraft travels in the still air at 200 m/sec, the velocity of discharge gases with respect to engine is 700 m/sec. The power developed by engine is
a) $7200\ kW\quad$ b) $5600\ kW\quad$ c) $2070\ kW\quad$ d) $4140\ kW$
My attempt:
Power of jet engine should be equal to the kinetic energy imparted to the discharge gases per unit time
$$=\frac{1}{2}(\text{mass flow rate of discharge gases})(\text{relative velocity of gases})^2$$
$$=\frac12(\dot m)(V_r)^2$$$$=\frac12(1+40)(700)^2\ J/sec$$$$=1004\ kW$$
My answer is not matching with any option. Can somebody please help me or suggest me where I am wrong? Thanks you very much.
The net force is:
$\text{Net force} = ( \dot m \cdot v)_{out} - ( \dot m \cdot v)_{in} $
$\text{Net force} = ( 41 \cdot 700)_{out} - ( 40 \cdot 200)_{in} $
$\text{Net force} = 28700 - 8000 $
$\text{Net force} = 20700 \text{N}$
**
The power developed is:
$\text{Power} = \text{Net force} \cdot \text{Plane velocity} $
$\text{Power} = 20700 \text{N} \cdot 200 \text{m/s} $
$\text{Power} = 4140 \text{kW} $