Question

The mass of a gas emitted from the rear of a toy rocket is initially 0.1kg/s. If the speed of the gas relative to the rocket is 50m/s, and the mass of the rocket is 2 kg, what is the initial acceleration of the rocket?

Answer 1

Solution

Rate of mass R=0.1Kg/sec

Speed of gas with relative to rocket v'=50m/s

Mass of rocket M=2Kg

Using momentum conservation

P= constant

$\frac{dP}{dt}=0$

For rocket P=Mv

v is velocity of rocket

$V\frac{dM}{dt}+M\frac{dv}{dt}=0$

$50\times 0.1+2a_r=0$

$a_r=-2.5m/s^2$