# A diwali rocket is ejecting 50 g of gases at velocity of 400m/s .the accelerating force on the rocket will be...???

##### 1 Answer

#### Answer:

#### Explanation:

I think that you mistyped the question.

More specifically, I think that the rocket actually ejects **per second** at a velocity of

That would make more sense, since *in total* would not make for a very impressive rocket.

So, the idea here is that the *constant rate* at which the gases are being ejected corresponds to the rocket's movement **at constant speed**.

If an object moves at *constant speed*, its acceleration, which is the **derivative of the speed** with respect to time, is equal to zero.

#d/dt(v) = a = 0 <=> v = "const"#

The speed of the rocket is constant, but its mass **is not**. This implies that its momentum will **not be constant**.

Assuming that the rocket flies *straight upward*, momentum is defined as

#P = m * v#

The momentum of the rocket *changes with respect to time* because the mass of the rocket changes with respect to time.

According to Newton's Second Law, the *rate of change* of the momentum of an object is *proportional* to the force that's acting on it.

In your case, this force will be the *ccelerating force*,

#d/dt(P) = d/dt(m * v)#

#F = d/dt(m * v)#

Use the product rule to differentiate this function

#F = d/dt(m) * v + m * underbrace(d/dt(v))_(color(blue)(=0))#

This means that

#F = v * underbrace(d/dt(m))_(color(blue)(="50 g/s"))#

To get the result in *Newtons*, convert the rate of change of the mass of the gases to

#50color(red)(cancel(color(black)("g")))/"s" * "1 kg"/(1000color(red)(cancel(color(black)("g")))) = "0.050 kg/s"#

The accelerating force will thus be

#F = 400"m"/"s" * 0.050"kg"/"s" = 20 "kg m"/"s"^2 = color(green)("20 N")#