StemCET Logo

Physics Question 87 – AP-EAMCET 2025

← Back
A machine gun with power 15 KW can fire 360 bullets per minute. If the mass of each bullet is 5 g, then the velocity of the bullets is

Power is the rate at which energy is transferred or converted. In this case, the power of the machine gun is used to impart kinetic energy to the bullets.

Step 1: Identify Given Parameters and Goal✦ Active

The problem provides the power of a machine gun, the rate at which it fires bullets, and the mass of each bullet. We need to find the velocity of the bullets. First, list the given values and convert them to SI units:

P=15 KW=15×103 W N=360 bullets per minute t=1 minute=60 s m=5 g=5×10−3 kg
💡 Teacher's Secret Hint

Always convert all given quantities to SI units (meters, kilograms, seconds, Watts) before performing calculations to avoid errors.

Step 2: Relate Power to Kinetic Energy○ Expand

The power of the machine gun is the rate at which it imparts kinetic energy to the bullets. The kinetic energy of a single bullet is KE=12mv2. If N bullets are fired in time t, the total kinetic energy imparted is N×12mv2. Therefore, the power P is given by:

P=Total Kinetic EnergyTime=N×12mv2t
💡 Teacher's Secret Hint

Remember that power is energy per unit time. For multiple objects, sum their individual energies.

Step 3: Substitute Values and Solve for Velocity○ Expand

Now, substitute the given values into the power equation and solve for the velocity v:

15×103 W=360×12(5×10−3 kg)v260 s 15×103=36060×12×(5×10−3)×v2 15×103=6×12×(5×10−3)×v2 15×103=3×(5×10−3)×v2 15×103=15×10−3×v2 v2=15×10315×10−3 v2=103×103 v2=106 v=106 v=103 m/s=1000 m/s

The velocity of the bullets is 1000 m/s.

💡 Teacher's Secret Hint

Simplify the numerical coefficients before dealing with powers of 10. This can make the calculation much cleaner.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.