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Answer :
Final answer:
To find the final speed of the lion-gazelle system after the attack, we can use the principles of conservation of momentum. By applying the equation for momentum and considering the initial momenta of the lion and the gazelle, we can calculate the final velocity of the lion-gazelle system. The final speed of the lion-gazelle system is 59.31 km/hr.
Explanation:
To find the final speed of the lion-gazelle system, we need to use the principles of conservation of momentum. The momentum of an object is defined as its mass multiplied by its velocity. In this case, the lion and the gazelle are separate objects, but they become a system after the lion attacks the gazelle.
To calculate the final speed of the lion-gazelle system, we can use the equation:
Momentum of lion before attack + Momentum of gazelle before attack = Momentum of lion-gazelle system after attack
Since momentum is a vector, we need to consider the direction of motion as well. The lion is running northward, so its velocity is positive, while the gazelle is running eastward, so its velocity is negative.
Let's calculate the momenta:
- The momentum of the lion before attack = mass of lion × velocity of lion = 181 kg × 71.9 km/hr = 13045.9 kg·km/hr
- The momentum of the gazelle before attack = mass of gazelle × velocity of gazelle = 30.8 kg × (-59.8 km/hr) = -1842.4 kg·km/hr
- Substituting the values into the equation, we have: 13045.9 kg·km/hr + (-1842.4 kg·km/hr) = (total mass of lion-gazelle system) × (final velocity of lion-gazelle system)
- Simplifying the equation, 13045.9 - 1842.4 = (total mass of lion-gazelle system) × (final velocity of lion-gazelle system)
- 11203.5 = (total mass of lion-gazelle system) × (final velocity of lion-gazelle system)
- Finally, dividing both sides by the total mass of the lion-gazelle system, we find the final velocity of the lion-gazelle system = 11203.5 / (181 + 30.8) = 59.31 km/hr
Therefore, the final speed of the lion-gazelle system, immediately after the attack, is 59.31 km/hr.
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