Final answer:
Using the conservation of momentum, we calculate that Matt's speed after catching his dog on the ice is approximately 2.04 m/s. We consider the momenta of both Matt and his dog before the catch and set it equal to the total momentum after the catch to find the final speed.
Step-by-step explanation:
The question at hand involves a scenario where Matt and his dog are playing around on ice and it relates to the conservation of momentum in physics. Given that Matt has a mass of 79.0 kg and is running at a speed of 2.90 m/s, and his dog has a mass of 30.0 kg running toward him at 1.25 m/s, we can solve for Matt's speed after catching his dog using the principle of conservation of momentum. The total momentum before the catch must equal the total momentum after the catch.
We assume a perfectly inelastic collision, as the dog stays in Matt's arms after being caught. We can now set up the equation: (mass of Matt × speed of Matt) + (mass of dog × speed of dog) = (combined mass) × (speed after the catch).
Putting the values into that equation gives us: (79.0 kg × 2.90 m/s) + (30.0 kg × 1.25 m/s) = (79.0 kg + 30.0 kg) × (speed after the catch).
To find Matt's speed just after he catches his dog, we solve for the 'speed after the catch' giving us:
(79.0 kg × 2.90 m/s + 30.0 kg × -1.25 m/s) / (79.0 kg + 30.0 kg) = 2.04 m/s.
Therefore, Matt's speed just after he catches his dog is approximately 2.04 m/s.