Two friends, Burt and Ernie, are standing at opposite ends of a uniform log that is floating in a lake. The log is 3.6 mm long and has mass 280 kgkg. Burt has mass 44.0 kgkg and Ernie has mass 34.0 kgkg. Initially the log and the two friends are at rest relative to the shore. Burt then offers Ernie a cookie, and Ernie walks to Burt's end of the log to get it.Part ARelative to the shore, what distance has the log moved by the time Ernie reaches Burt? Neglect any horizontal force that the water exerts on the log and assume that neither Burt nor Ernie falls off the log.Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typex𝑥 =

To solve this problem, we need to use the principle of conservation of momentum. The total momentum of the system (Burt, Ernie, and the log) before Ernie starts moving is zero, because they are all at rest. The total momentum of the system after Ernie moves should also be zero, because there are no external forces acting on the system.

Before Ernie moves, the center of mass of the system is at the center of the log, because the log is uniform and Burt and Ernie are at opposite ends. After Ernie moves, the center of mass of the system is still at the same place, because the total momentum of the system has not changed.

Let's denote the distance that the log moves by x. The distance that Ernie moves is the length of the log, 3.6 m. The distance that the center of mass of the system moves is zero, because the total momentum of the system has not changed.

We can set up the following equation based on the definition of the center of mass:

(mass of Burt * distance Burt moves) + (mass of Ernie * distance Ernie moves) + (mass of log * distance log moves) = total mass * distance center of mass moves

Substituting the given values and solving for x, we get:

(44.0 kg * 0) + (34.0 kg * 3.6 m) + (280 kg * x) = (44.0 kg + 34.0 kg + 280 kg) * 0

Solving for x, we get:

x = - (34.0 kg * 3.6 m) / 280 kg = -0.438 m

The negative sign indicates that the log moves in the opposite direction to Ernie. So, the log moves 0.438 m towards Burt.