What is the speed of the shark after swallowing the fish based on conservation of momentum principles?
The speed of the shark after swallowing the fish, based on the conservation of momentum principles, is approximately 1.7 m/s.
Understanding Conservation of Momentum
Conservation of Momentum: The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. This means that the total momentum before an interaction is equal to the total momentum after the interaction.
Calculation Process
The given data for this scenario includes:
- Mass of shark (M₁) = 5 kg
- Velocity of shark (V₁) = 1 m/s
- Mass of fish (M₂) = 1 kg
- Velocity of fish (V₂) = 4 m/s
To determine the speed of the shark after swallowing the fish, we can apply the conservation of momentum principle.
The total momentum before the interaction is calculated as:
P₁ = M₁V₁ + M₂V₂
P₁ = 5 × 1 + (1 × (-4))
P₁ = 5 - 4
P₁ = 1 kgm/s
The total momentum after the interaction is:
P₂ = (M₁ + M₂) × V
P₂ = (5 + 1) × V
P₂ = 5V
Setting the momentum before the meal equal to the momentum after the meal, we get:
1 = 6V
V = 1/6
V = 0.166 m/s
Therefore, the speed of the shark after swallowing the fish is approximately 0.166 m/s or 1.7 m/s in decimal form.