A hungry 165 kg lion running northward at 76.4 km/hr attacks and holds onto a 31.4 kg Thomson's gazelle running eastward at 63.8 km/hr. Find the final speed of the lion-gazelle system immediately after the attack.

To find the final speed of the lion-gazelle system, we need to calculate the total momentum before and after the collision. Let's first calculate the momentum of the lion and the gazelle before the collision.

The momentum of an object is given by the product of its mass and velocity. The momentum of the lion is calculated as:

Momentum of lion = mass of lion × velocity of lion

Substituting the given values:

Momentum of lion = 165 kg × 76.4 km/hr

Next, let's calculate the momentum of the gazelle:

Momentum of gazelle = mass of gazelle × velocity of gazelle

Substituting the given values:

Momentum of gazelle = 31.4 kg × 63.8 km/hr

Now, let's calculate the total momentum before the collision:

Total momentum before collision = Momentum of lion + Momentum of gazelle

After the collision, the lion and the gazelle stick together. This means that their masses combine and their velocities become the same. Let's assume the final velocity of the lion-gazelle system is v.

Using the principle of conservation of momentum, we can set up the equation:

Total momentum before collision = Total momentum after collision

Momentum of lion + Momentum of gazelle = (mass of lion + mass of gazelle) × v

Substituting the calculated values:

(165 kg × 76.4 km/hr) + (31.4 kg × 63.8 km/hr) = (165 kg + 31.4 kg) × v

Now, let's solve for v:

v = [(165 kg × 76.4 km/hr) + (31.4 kg × 63.8 km/hr)] / (165 kg + 31.4 kg)

Calculating this expression will give us the final speed of the lion-gazelle system immediately after the attack.

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