Due to internal combustion inside a rocket, gases are ejected at the rate of $2.4 kg / minute$ . The velocity of the gases with respect to the rocket is $400 m / s$ . Calculate the force exerted on the rocket.

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Solution

Step 1: Given data
Rate of ejection of gases or rate of change of the mass = $\frac{d m}{d t} = 2.4 K g / m i n u t e$
The velocity of gases with respect to the rocket = $v = 400 m / s$
Step 2: Formula used
Rate of change of momentum = $v (\frac{d m}{d t})$
Step 3: Calculation
By substituting the values in the above formula, we get
$T h e r a t e o f c h a n g e o f t h e m o m e n t u m = v (\frac{d m}{d t}) = (400 m / s e c) \times (\frac{2.4}{60} k g / s e c)$
Since force is equivalent to momentum.
$F o r c e = R a t e o f c h a n g e o f m o m e n t u m = v (\frac{d m}{d t}) = 400 \times \frac{2.4}{60} = 16 N$
Therefore force exerted on the rocket is $16 N$ .

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Due to internal combustion inside a rocket, gases are ejected at the rate of 2.4kg/minute. The velocity of the gases with respect to the rocket is 400m/s. Calculate the force exerted on the rocket.

Due to internal combustion inside a rocket, gases are ejected at the rate of $2.4 kg / minute$ . The velocity of the gases with respect to the rocket is $400 m / s$ . Calculate the force exerted on the rocket.