Final answer:
The sled will continue moving with a velocity of 8.4 m/s after the dog jumps off.
Step-by-step explanation:
To answer this question, we can apply the principle of conservation of momentum. The momentum of an object is given by the product of its mass and velocity. Since momentum is conserved in the absence of external forces, the initial momentum of the system (dog + sled) must be equal to the final momentum of the system.
Initially, the dog and sled are moving together, so their initial momentum is the sum of their individual momenta. The momentum of the dog is given by the product of its mass (4.8 kg) and initial velocity (2.0 m/s), while the momentum of the sled is the product of its mass (1.5 kg) and initial velocity (2.0 m/s).
To find the final velocity of the sled, we equate the initial momentum of the system to the final momentum of the sled. The mass of the dog is not relevant, since it has jumped off the sled and no longer contributes to the momentum. Therefore, the final momentum of the sled is the product of its mass (1.5 kg) and final velocity (v).
Using the principle of conservation of momentum, we can write:
(4.8 kg)(2.0 m/s) + (1.5 kg)(2.0 m/s) = (1.5 kg)(v)
Simplifying the equation, we have:
9.6 kg·m/s + 3.0 kg·m/s = 1.5 kg·v
12.6 kg·m/s = 1.5 kg·v
Dividing both sides of the equation by 1.5 kg, we find:
v = 8.4 m/s
The sled will continue moving with a velocity of 8.4 m/s after the dog jumps off.