Answer:
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
