Answer :
The final speed of the lion-gazelle system immediately after the attack is 17.23 m/s.
The final speed of the lion-gazelle system immediately after the attack can be found by using the principle of conservation of momentum.
First, we need to convert the masses and speeds of the lion and gazelle from km/hr to m/s.
The lion's mass is 181 kg and its speed is 75.5 km/hr. Converting this to m/s, we get 75.5 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 20.97 m/s.
The gazelle's mass is 39.2 kg and its speed is 56.6 km/hr. Converting this to m/s, we get 56.6 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 15.72 m/s.
Next, we can calculate the initial momentum of the system. The lion's momentum is given by mass times speed, so 181 kg * 20.97 m/s = 3790.57 kg·m/s. The gazelle's momentum is 39.2 kg * 15.72 m/s = 615.46 kg·m/s.
Since the gazelle is initially at rest, its momentum is zero. Therefore, the initial momentum of the system is 3790.57 kg·m/s + 0 kg·m/s = 3790.57 kg·m/s.
After the attack, the lion and gazelle move together as one system. Therefore, their final momentum will be the same as the initial momentum of the system.
To find the final speed of the lion-gazelle system, we divide the total momentum by the combined mass of the lion and gazelle. The combined mass is 181 kg + 39.2 kg = 220.2 kg.
So, the final speed of the lion-gazelle system immediately after the attack is 3790.57 kg·m/s / 220.2 kg = 17.23 m/s.
In summary, the final speed of the lion-gazelle system immediately after the attack is 17.23 m/s.
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The complete question is:
A hungry 161-kg lion running northward at 75.5 km/hr attacks and holds onto a 35.9-kg Thomson\'s gazelle running eastward at 61.4 km/hr. Find the final speed of the lion-gazelle system, immediately after the attack.
