Lillian (mass 46.0 Kg) standing on slippery ice catches her leaping dog (mass 15 kg) moving horizontally at 4.0 m/s. What is the speed of lillian and her dog after the catch.

momentumdoginitial=momenumCombinationafter
15*4=(46 +15)v
solve for v.

60/61

To solve this problem, we need to apply the law of conservation of momentum.

The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, as long as there are no external forces acting on the system.

In this case, the initial momentum of the dog is given by the product of its mass and velocity: momentum_dog_initial = mass_dog * velocity_dog = 15 kg * 4.0 m/s = 60 kg·m/s.

After catching the dog, the momentum of the combined system (Lillian + dog) will be the same as the initial momentum of the dog.

Let's denote the final velocity of Lillian and her dog after the catch as v_combination.

Using the conservation of momentum, we can write the equation:

momentum_dog_initial = momentum_combination_after

60 kg·m/s = (46 kg + 15 kg) * v_combination

Combining the masses on the right side of the equation, we get:

60 kg·m/s = 61 kg * v_combination

To solve for v_combination, we divide both sides of the equation by 61 kg:

v_combination = 60 kg·m/s / 61 kg ≈ 0.98 m/s

Therefore, the speed of Lillian and her dog after the catch is approximately 0.98 m/s.