Question 12 of 19 Lions can run at speeds up to approximately 80.0 km/h. A hungry 109 kg lion running northward at top speed attacks and holds onto a 36.0 kg Thomson's gazelle running eastward at 78.0 km/h. Find the final speed vf of the lion‑gazelle system just after the lion attacks.

The final velocity of the lion-gazelle system is approximately 62.321 kilometers per hour.

Explanation:

Let suppose that both lion and the Thomson's gazelle collide each other inelastically, the use of the Principle of Linear Momentum Conservation suffices to describe the entire phenomenon:

(1)

Where:

- Mass of the lion, in kilograms.

- Mass of the Thomson's gazelle, in kilograms.

- Initial velocity of the lion, in meters per second.

- Initial velocity of the Thomson's gazelle, in meters per second.

- Final velocity of the lion-gazelle system, in meters per second.

Let suppose that both northward velocity and eastward velocity are positive.

If we know that , , and , then the final velocity of the lion-gazelle system is:

And the final speed of the lion-gazelle system is calculated by the Pythagorean Theorem:

The final velocity of the lion-gazelle system is approximately 62.321 kilometers per hour.

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