Question

A machine gun fires 240 bullets per minute with certain velocity. If the mass of each bullet is 10^-2kg and the power of the gun is 7.2kW, find the velocity with each bullet is fired.(Power=n(1/2mv^2)/t)​

Answer 1

Given:-

→ No. of bullets fired = 240

→ Time = 1 min = 60s

→ Mass of each bullet = 10⁻² kg

→ Power of the gun = 7.2 kW

To find:-

→ Velocity with which each bullet is fired.

Solution:-

Firstly, let's convert the power of the gun from kW to W.

⇒ 1 kw = 1000 W

⇒ 7.2 kW = 7.2(1000)

⇒ 7200 W

________________________________

We know that :-

Work done = ∆K.E.

Work done by each bullet will be :-

⇒ W = ½mv² - ½mu²

⇒ W = ½×10⁻²×v² - ½×10⁻²×0

⇒ W = ½×0.01×v²

⇒ W = 0.005v²

∴ Work done by 240 bullets :-

⇒ W' = 0.005v²×240

⇒ W' = 1.2v²

________________________________

Now, we know that :-

Power = Work done/Time taken

Thus, in this case :-

⇒ P = W'/t

⇒ 7200 = 1.2v²/60

⇒ v² = 7200×60/1.2

⇒ v² = 432000/1.2

⇒ v² = 360000

⇒ v = √360000

⇒ v = 600 m/s

Thus, each bullet is fired with a velocity of 600m/s .