Answer :
The final speed of the lion-gazelle system immediately after the attack is approximately 21.26 m/s.
the final speed of the lion-gazelle system immediately after the attack is approximately 21.26 m/s.The final speed of the lion-gazelle system immediately after the attack can be found by applying the principle of conservation of momentum.
To begin, let's convert the speeds of the lion and the gazelle from km/hr to m/s. We know that 1 km/hr is equal to 0.2778 m/s.
The lion's speed is 80.9 km/hr, so we can calculate it as follows:
Speed of the lion = 80.9 km/hr × 0.2778 m/s
Speed of the lion = 22.47 m/s
Similarly, the gazelle's speed is 55.0 km/hr, which is:
Speed of the gazelle = 55.0 km/hr × 0.2778 m/s
Speed of the gazelle = 15.28 m/s
Now, let's analyze the directions of motion. The lion is running northward, which we can consider as the positive y-direction. The gazelle is running eastward, which we can consider as the positive x-direction.
The momentum of an object is given by its mass multiplied by its velocity. Let's calculate the initial momentum of the lion and the gazelle separately.
Momentum of the lion = mass of the lion × speed of the lion
Momentum of the lion = 165 kg × 22.47 m/s
Momentum of the lion = 3706.55 kg·m/s
Momentum of the gazelle = mass of the gazelle × speed of the gazelle
Momentum of the gazelle = 32.9 kg × 15.28 m/s
Momentum of the gazelle = 503.51 kg·m/s
Since momentum is a vector quantity, we need to consider the direction as well. The momentum of the lion can be considered positive in the y-direction, while the momentum of the gazelle is positive in the x-direction.
Now, let's find the total momentum of the system before the attack. Since the lion and the gazelle are not influenced by external forces, the total momentum before the attack is equal to the total momentum after the attack.
Total momentum before the attack = Total momentum after the attack
Let's denote the final speed of the lion-gazelle system as V. Using the conservation of momentum, we can write:
Momentum of the lion after the attack + Momentum of the gazelle after the attack = Total momentum after the attack
Since the lion holds onto the gazelle, their final momentum will be the same.
(165 kg + 32.9 kg) × V = 3706.55 kg·m/s + 503.51 kg·m/s
197.9 kg × V = 4210.06 kg·m/s
Now, let's solve for V:
V = (4210.06 kg·m/s) / (197.9 kg)
V ≈ 21.26 m/s
Therefore, the final speed of the lion-gazelle system immediately after the attack is approximately 21.26 m/s.
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