Answer :
Using the law of conservation of momentum, we find that the lion's momentum is 12161.1 kg*km/hr and the gazelle's momentum is 2048.62 kg*km/hr. The total momentum, calculated using Pythagoras' theorem, is 12415.5 kg*km/hr. The final speed of the lion-gazelle system is 65.9 km/hr.
The final speed of the lion-gazelle system can be found using the law of conservation of momentum. This law states that the total momentum of a system remains constant if no external forces act on it.
Given the initial momentum of both the lion and the gazelle, we can find their final velocity.
The lion's momentum is its mass times its velocity: 169 kg * 71.9 km/hr = 12161.1 kg*km/hr. The gazelle's momentum is 31.7 kg * 64.6 km/hr = 2048.62 kg*km/hr.
As they are at right angles, we use Pythagoras' theorem to find the resultant: √(12161.1^2 + 2048.62^2) = 12415.5 kg*km/hr. This is the total momentum of the system.
The final speed is the total momentum divided by the total mass: 12415.5 kg*km/hr / (169 kg + 31.7 kg) = 65.9 km/hr.
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Final answer:
The final speed of the lion-gazelle system immediately after the attack can be found by applying the principle of conservation of momentum. The lion's momentum before the collision plus the gazelle's momentum before the collision is equal to the total momentum after the collision. By solving the equation, we can determine the final speed of the lion-gazelle system.
Explanation:
To find the final speed of the lion-gazelle system after the attack, we need to apply the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Let's consider the lion's velocity as positive since it is running northward, and the gazelle's velocity as negative since it is running eastward.
The momentum of an object is calculated by multiplying its mass by its velocity. The momentum of the lion before the collision is given by:
Momentum of lion before collision = mass of lion × velocity of lion
Momentum of lion before collision = 169 kg × 71.9 km/hr
Similarly, the momentum of the gazelle before the collision is:
Momentum of gazelle before collision = mass of gazelle × velocity of gazelle
Momentum of gazelle before collision = 31.7 kg × (-64.6 km/hr)
Since the lion and gazelle stick together after the collision, their final velocity will be the same. Let's assume the final velocity of the lion-gazelle system is V.
The total momentum after the collision is:
Total momentum after collision = (mass of lion + mass of gazelle) × V
Using the principle of conservation of momentum, we can equate the total momentum before and after the collision:
Momentum of lion before collision + Momentum of gazelle before collision = Total momentum after collision
169 kg × 71.9 km/hr + 31.7 kg × (-64.6 km/hr) = (169 kg + 31.7 kg) × V
Solving this equation will give us the value of V, which represents the final speed of the lion-gazelle system after the attack.
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