Question

A 1000-kg space probe is motionless in space. To start moving its main engine is fired for 5 sec during wohi hn it ejects exhaust gases at 5000 m/s at the end of this process it's moving with the speed of 20 m/s. What is the approximate mass of ejected gases?

Answer 1

$we \: know \: mass \: of \: probe \: = 1000 \: kg \\ \\ initial \: velocity \: of \: probe \: = 0 \: \frac{m}{s} \\ \\ speed \: of \: gases \: = 5000 \: \: \frac{m}{s} \\ \\ speed \: of \: probe \: = 20 \: \frac{m}{s} \\ \\ according \: to \: law \: of \: conservation \: of \: momentum \\ \\ change \: in \: momentum \: will \: be \: same \: \\ \\ 1000 \times 20 \frac{m}{s} = mass \: of \: gas \times 5000 \frac{m}{s} \\ mass \: of \: gas \: = \frac{20000}{5000} = 4 \: kg$

Answer 2

Given:

Mass of probe : $1000kg$  

Engine fired time:$5 sec$  

Speed of gases: $5000m/s$  

Speed of probe: $20 m/s.$

To find:

Mass of ejected gases  

Step by step explanation:

According to law of conservation of momentum change in momentum,  

           Mass of probe $\times$ Speed of probe $=$ Mass of gas $\times$ Speed of gas  

then, substitute  the all values in this formula  

we get,

               $1000\times20=$ Mass of gas$\times5000$    

                         $20000=$Mass of gas$\times5000$  

                          $\frac{20000}{5000}=$ Mass of gas

                                $4=$ Mass of gas

Mass of the ejected gases is  $4m/s$