A 64.8 kg ice skater is skating along in a straight line (in the positive direction) at 9.2 m/s when he bends down and scoops up his 24.4 kg doggy sitting still on the ice. What will be the new velocity of the dog-n-skater?

M1*V1 + M2*V2 = M1*V + M2*V,

64.8*9.2 + 24.4*0 = 64.8V + 24.4V, 596.16 = 89.2V, V = 6.68 m/s.

To find the new velocity of the dog-n-skater after the skater scoops up the dog, we can use the principle of conservation of momentum.

The initial momentum of the skater before picking up the dog is given by:
Initial momentum(skater) = mass(skater) * velocity(skater)

The initial momentum of the dog before being scooped up is zero since it is sitting still.

Therefore, the initial total momentum is just the momentum of the skater:
Initial total momentum = Initial momentum(skater) = mass(skater) * velocity(skater)

After picking up the dog, the skater and the dog move together as a system. The final total momentum of the system is given by:
Final total momentum = mass(skater+dog) * velocity(final)

Since momentum is conserved, the initial total momentum is equal to the final total momentum:
Initial total momentum = Final total momentum

Therefore, we have:
mass(skater) * velocity(skater) = mass(skater+dog) * velocity(final)

Plugging in the given values:
mass(skater) = 64.8 kg
velocity(skater) = 9.2 m/s
mass(dog) = 24.4 kg

We can rearrange the equation to solve for velocity(final):
velocity(final) = (mass(skater) * velocity(skater)) / mass(skater+dog)

Substituting the values:
velocity(final) = (64.8 kg * 9.2 m/s) / (64.8 kg + 24.4 kg)

Calculating the result:
velocity(final) = 601.44 kg*m/s / 89.2 kg

velocity(final) ≈ 6.74 m/s

Therefore, the new velocity of the dog-n-skater after scooping up the dog will be approximately 6.74 m/s in the positive direction.

To determine the new velocity of the dog-n-skater system after the skater scoops up the dog, we need to apply the law of conservation of momentum.

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it.

The momentum of an object is given by the product of its mass and velocity. So, the initial momentum of the skater can be calculated as:

Initial momentum of skater = mass of skater × initial velocity of skater

= 64.8 kg × 9.2 m/s

= 595.36 kg·m/s

The initial momentum of the dog is zero since it is sitting still.

Thus, the initial momentum of the dog-n-skater system is equal to the initial momentum of the skater alone.

Now, when the skater scoops up the dog, the total mass of the system becomes the sum of the masses of the skater and the dog:

Total mass of the system = mass of skater + mass of dog

= 64.8 kg + 24.4 kg

= 89.2 kg

Since no external forces act on the system, the total momentum remains constant. Therefore, the final momentum of the system is also equal to the initial momentum.

Final momentum of system = Total mass of system × final velocity of system

To find the final velocity of the dog-n-skater system, we can rearrange the equation:

Final velocity of system = Final momentum of system / Total mass of system

Since the final momentum is equal to the initial momentum, we can substitute the initial momentum and rearrange the equation:

Final velocity of system = Initial momentum of system / Total mass of system

= 595.36 kg·m/s / 89.2 kg

= 6.68 m/s

Therefore, the new velocity of the dog-n-skater system after the skater scoops up the dog is 6.68 m/s in the positive direction.