A hungry 181 kg lion running northward at 71.0 km/hr attacks and holds onto a 38.6 kg Thomson's gazelle running eastward at 63.8 km/hr. Find the final speed of the lion–gazelle system immediately after the attack.

16.5514 m/sec

Explanation:

The conservation of momentum is the way to solve this problem.

The pre-collision momentum of the lion is

p₁ = 181 kg (19.7222 m/s), north = 3569.7222 kg m/sec, north

The pre-collision momentum of the gazelle is

p₂ = 38.6 kg (17.7222 m/s), east = 684.0778 kg m/sec, east

The magnitude of the momentum vector of the lion-gazelle system after the collision is

P = √(p₁² + p₂²) = 3634.6773 kg m/sec

The magnitude of the velocity vector of the lion-gazelle system after the collision is

v = P/(M₁ + M₂) = 16.5514 m/sec

The direction of these vectors is found from

θ = arctan[p₁/p₂] = 79.151737° north of east

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