Question

A 800 kg rocket is fired from earth so that exhaust speed is 1200 m/s. Then calculate mass of fuel burning per second, to provide initial thrust to overcome its weight. (g = 10 m/s²).

Answer 1

20/3 kg/s

Answer 2

The thrust force ($F_{thrust}$) generated by a rocket is given by the product of the mass ejection rate ($\frac{\Delta m}{\Delta t}$) and the exhaust velocity ($v$): $F_{thrust} = \frac{\Delta m}{\Delta t} v$ To overcome its weight ($W = mg$), the initial thrust must be equal to the weight. This implies that the net force on the rocket is zero, and therefore, the initial acceleration ($a$) is zero. $F_{thrust} = W$ Substituting the expressions for thrust and weight: $\frac{\Delta m}{\Delta t} v = mg$ Solving for the mass ejection rate (mass of fuel burning per second): $\frac{\Delta m}{\Delta t} = \frac{mg}{v}$ Substituting the given values: $m = 800$ kg $g = 10$ m/s$^2$ $v = 1200$ m/s $\frac{\Delta m}{\Delta t} = \frac{(800 \text{ kg})(10 \text{ m/s}^2)}{1200 \text{ m/s}} = \frac{8000}{1200} \text{ kg/s} = \frac{80}{12} \text{ kg/s} = \frac{20}{3} \text{ kg/s}$