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Answer :
According to the question the final speed of the lion-gazelle system immediately after the attack is approximately 21.3 m/s.
To find the final speed of the lion-gazelle system immediately after the attack, we can apply the principle of conservation of momentum. The total momentum before the attack is equal to the total momentum after the attack.
First, we need to convert the speeds of the lion and the gazelle from km/hr to m/s:
Lion's speed: 80.0 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 22.2 m/s
Gazelle's speed: 60.6 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 16.8 m/s
The momentum of an object is given by its mass multiplied by its velocity. Therefore, the initial momentum of the lion is 173 kg * 22.2 m/s = 3834.6 kg·m/s, and the initial momentum of the gazelle is 32.3 kg * 16.8 m/s = 542.64 kg·m/s.
Since the lion holds onto the gazelle after the attack, their momenta are combined. The final momentum of the lion-gazelle system is the sum of their individual momenta.
Final momentum = 3834.6 kg·m/s + 542.64 kg·m/s = 4377.24 kg·m/s
To find the final speed of the lion-gazelle system, we divide the total momentum by the total mass of the system:
Total mass = 173 kg + 32.3 kg = 205.3 kg
Final speed = Final momentum / Total mass = 4377.24 kg·m/s / 205.3 kg ≈ 21.3 m/s
Therefore, the final speed of the lion-gazelle system immediately after the attack is approximately 21.3 m/s.
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