Complete question:
The recoil of a shotgun can be significant. Suppose a 3.6-kg shotgun is held tightly by an arm and shoulder with a combined mass of 15.0 kg. When the gun fires a projectile with a mass of 0.040 kg and a speed of 380 m/s, what is the recoil velocity of the shotgun and arm–shoulder combination?
Answer:
The recoil velocity of the shotgun and arm–shoulder combination is 1.013 m/s
Explanation:
Given;
combined mass of the shotgun and arm–shoulder, m₁ = 15 kg
mass of the projectile, m₂ = 0.04 kg
speed of the projectile, u₂ = 380 m/s
let the recoil velocity of the shotgun and arm–shoulder combination = u₁
Apply the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = 0
m₁u₁ = - m₂u₂

Therefore, the recoil velocity of the shotgun and arm–shoulder combination is 1.013 m/s
The law of conservation tells us that no mass is lost. This is true because when wood burns or turns into ash, some of it is escaped as gases like carbon dioxide and water vapor into air . If we calculate the mass of these atmospheric gases that evolved when the wood turned into ash, we would find that the total mass of all these substances including the ash is equal to the log of wood.
The acceleration experienced by the particle is given by

This corresponds to the centripetal acceleration of the motion, which is related to the angular speed

of the particle and its distance r from the axis by the relationship

In our problem,

, so we can solve for

:

However, we must convert it into rpm (revolution per minute).
We know that 1 rad corresponds to

revolutions, while

. So we the conversion is
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