Answer: To solve this problem, we need to use the principle of conservation of momentum, which states that the total momentum of a system before a collision is equal to the total momentum after the collision, assuming that there are no external forces acting on the system.
The initial momentum of the system (Sally and the sled) is:
p1 = m1v1 + m2v2
where m1 = 68 kg is Sally's mass, v1 = 3 m/s is her velocity before jumping on the sled, m2 = 6 kg is the mass of the sled, and v2 = 0 m/s is the velocity of the sled before the collision (at rest).
Therefore, the initial momentum is:
p1 = (68 kg)(3 m/s) + (6 kg)(0 m/s) = 204 kg·m/s
After Sally jumps on the sled, the combined mass of Sally and the sled is:
m = m1 + m2 = 68 kg + 6 kg = 74 kg
Let's assume that the combined velocity of Sally and the sled after the collision is v. Then, we can write the final momentum of the system as:
p2 = mv
According to the conservation of momentum principle, p1 = p2. Therefore:
m1v1 + m2v2 = mv
Substituting the values, we get:
(68 kg)(3 m/s) + (6 kg)(0 m/s) = (74 kg) v
Solving for v, we get:
v = (68 kg)(3 m/s) / (74 kg) = 2.77 m/s
Therefore, the combined velocity of Sally and the sled right after she jumps on it is 2.77 m/s (rounded to two decimal places).
Step-by-step explanation: