To find the total momentum of the three dogs, we first need to understand the concept of momentum itself. Momentum is defined as the product of an object's mass and its velocity. The formula for momentum (p) is given by:
p = m × v
Where:
- p is the momentum
- m is the mass of the object
- v is the velocity of the object
In this scenario, we have two puppies and one older dog. Let's break down the calculations step by step.
Step 1: Calculate the momentum of each dog
First, we will calculate the momentum for each dog individually:
Puppies
Each puppy has a mass of 4.00 kg and runs at a speed of 1.10 m/s. The momentum for one puppy is:
p_puppy = m × v = 4.00 kg × 1.10 m/s = 4.40 kg·m/s
Since there are two puppies, we multiply this value by 2:
Total momentum of puppies = 2 × 4.40 kg·m/s = 8.80 kg·m/s
Older Dog
The older dog has a mass of 9.00 kg and runs at a speed of 1.30 m/s. The momentum for the older dog is:
p_older_dog = m × v = 9.00 kg × 1.30 m/s = 11.70 kg·m/s
Step 2: Combine the momenta
Now that we have the momenta for both the puppies and the older dog, we can find the total momentum:
Total momentum = Total momentum of puppies + Momentum of older dog
Total momentum = 8.80 kg·m/s + 11.70 kg·m/s = 20.50 kg·m/s
Step 3: Determine the direction
Assuming all dogs are running towards the food in the same direction, the total momentum will also be in that direction. Therefore, the direction of the total momentum is the same as the direction in which the dogs are running.
Final Result
The magnitude of the total momentum of the three dogs is 20.50 kg·m/s, and the direction is towards the food they are running to.
