A 77.6 kg ice skater is skating along in a straight line (in the positive direction) at 10.3 m/s when he bends down and scoops up his 27.4 kg doggy sitting still on the ice. What will be the new velocity of the dog-n-skater?
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To find the new velocity of the dog-n-skater system, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after an interaction remains the same, assuming no external forces act on the system.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the initial momentum of the skater can be calculated as the product of the skater's mass (77.6 kg) and the initial velocity (10.3 m/s), which is equal to (77.6 kg) x (10.3 m/s) = 799.28 kg*m/s.
The dog is initially at rest, so its momentum is zero.
When the skater bends down and scoops up the dog, their momenta combine to form the new momentum of the system. The momentum of the skater and the dog-n-skater system will be the same because they both experience the same force and acceleration.
The mass of the system after scooping up the dog is the sum of the masses of the skater and the dog, which is (77.6 kg + 27.4 kg) = 105 kg.
To find the new velocity of the system, we can divide the initial momentum by the new total mass. Therefore, the new velocity of the dog-n-skater system is (799.28 kg*m/s) / (105 kg) = 7.61 m/s.
So, the new velocity of the dog-n-skater system after scooping up the dog will be 7.61 m/s in the positive direction.