A gun weighing 4kg fires a bullet with a velocity 50ms-1. If the weight of the bullet is 15g, find the recoil velocity of the gun.
Question
A gun weighing 4kg fires a bullet with a velocity 50ms-1. If the weight of the bullet is 15g, find the recoil velocity of the gun.
Solution
Sure, here's how you can solve this problem:
Step 1: Understand the problem The problem is asking for the recoil velocity of the gun. According to Newton's third law, the gun should recoil with an equal and opposite momentum to the bullet.
Step 2: Convert the weight of the bullet to kg The weight of the bullet is given in grams. We need to convert it to kilograms to match the unit of the gun's weight. So, 15g = 0.015kg.
Step 3: Calculate the momentum of the bullet Momentum is calculated as the product of mass and velocity. So, the momentum of the bullet is 0.015kg * 50m/s = 0.75 kg*m/s.
Step 4: Calculate the recoil velocity of the gun The gun should recoil with an equal and opposite momentum to the bullet. So, the recoil velocity of the gun is the momentum of the bullet divided by the mass of the gun. So, the recoil velocity is 0.75 kg*m/s / 4kg = 0.1875 m/s.
So, the recoil velocity of the gun is 0.1875 m/s.
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