Final answer:
The total momentum of the lion and the gazelle is 4228.75 kg m/s.
Step-by-step explanation:
The total momentum of the lion and the gazelle can be calculated by adding together their individual momenta. The momentum of an object is given by the product of its mass and velocity. To solve this problem, we need to convert the speeds of the lion and gazelle from km/hr to m/s.
First, let's calculate the momentum of the lion. The lion has a mass of 161 kg and is running northward at a speed of 81.8 km/hr. Converting this speed to m/s, we get:
81.8 km/hr = (81.8 × 1000) / 3600 m/s = 22.73 m/s
Now, we can calculate the momentum of the lion:
Momentum of the lion = mass × velocity = 161 kg × 22.73 m/s = 3651.53 kg m/s
Next, let's calculate the momentum of the gazelle. The gazelle has a mass of 36.8 kg and is running eastward at a speed of 56.6 km/hr. Converting this speed to m/s, we get:
56.6 km/hr = (56.6 × 1000) / 3600 m/s = 15.72 m/s
Now, we can calculate the momentum of the gazelle:
Momentum of the gazelle = mass × velocity = 36.8 kg × 15.72 m/s = 577.22 kg m/s
To find the total momentum of the lion and gazelle, we simply add the two momenta:
Total momentum = 3651.53 kg m/s + 577.22 kg m/s = 4228.75 kg m/s