Momentum is a vector quantity given by the product of an object's mass and velocity. It has both magnitude and direction. In this scenario, we have three objects with given masses and velocities. It's important to note that momentum in the opposite direction (westward) will have a different sign than momentum in the eastward direction.
Let's calculate the momentum for each object and then the total momentum of the system.
Object m₁:
- Mass (m₁) = 12 kg
- Velocity (v₁) = 120 m/s eastward
The momentum (p₁) for the first object is calculated as:
p₁ = m₁ * v₁
= 12 kg * 120 m/s
= 1440 kg·m/s eastward
Object m₂:
- Mass (m₂) = 25 kg
- Velocity (v₂) = 18 m/s westward
Since the second object is moving westward, its velocity is in the opposite direction, we consider this as negative in our calculation.
The momentum (p₂) for the second object is calculated as:
p₂ = m₂ * v₂
= 25 kg * (-18 m/s)
= -450 kg·m/s (the negative sign indicates the westward direction)
Object m₃:
- Mass (m₃) = 1 kg
- Velocity (v₃) = 350 m/s eastward
The momentum (p₃) for the third object is calculated as:
p₃ = m₃ * v₃
= 1 kg * 350 m/s
= 350 kg·m/s eastward
Now, to find the total momentum of the system, we sum the individual momenta, keeping in mind to take into account their signs as they indicate direction.
Total momentum (p_total) = p₁ + p₂ + p₃
= 1440 kg·m/s (eastward) - 450 kg·m/s (westward) + 350 kg·m/s (eastward)
Since momentum in the westward direction is negative, we subtract it in our calculation.
So the total momentum of the system is:
p_total = 1440 kg·m/s + 350 kg·m/s - 450 kg·m/s
= 1340 kg·m/s + (-450 kg·m/s)
= 890 kg·m/s
The positive sign of the result indicates that the total momentum of the system is directed eastward. Therefore, the total momentum of the system is 890 kg·m/s in the eastward direction.
