Answer:
77.9 km/h
Explanation:
We determine the initial momenta of lion and gazelle.
Lion: 173 × 80.9 = 13995.7
Gazelle: 36.2 × 63.8 = 2309.56
Since they are running in the same direction, we add their momenta to get the total initial momentum:
[tex]p_1 = 13995.7+2309.56 = 16305.26[/tex]
After the collision, they are together and have a common velocity. Hence, the total final momentum is
[tex]p_2 = (173+36.2)\times v = 209.2v[/tex]
By the principle of conservation of momentum, the total initial momentum is equal to the total final momentum, provided there are no external forces.
[tex]209.2v = 16305.26[/tex]
[tex]v = \dfrac{16305.26}{209.2} = 77.9 \text{ km/h}[/tex]
