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]