The amount that the springs are stretched depends on the force that is pulling them apart. In each scenario, the force pulling the springs apart is the weight of Grogg and the sled.

In scenario A, the sled is stationary, so there is no force pulling the springs apart. Therefore, the springs are not stretched at all.

In scenario B, the sled is moving forward at constant speed, so there is no net force acting on it. The force of friction is counteracted by the force of the sled pushing back on the ground. Therefore, the springs are not stretched in this scenario either.

In scenario C, the sled is slowing down, so there is a net force acting on it. The force of friction is greater than the force of the sled pushing back on the ground. Therefore, the springs are stretched in this scenario.

In scenario D, Grogg is going down a ramp, so there is a force pulling him down the ramp. This force is greater than the force of friction, so the springs are stretched in this scenario.

In scenario E, Grogg is going up a ramp, so there is a force pulling him up the ramp. This force is less than the force of friction, so the springs are not stretched in this scenario.

Therefore, the ranking of the scenarios in terms of how much the springs are stretched is:

A. The sled is stationary and the ground is flat.

B. The sled slides forward across the ground at constant speed; there is negligible friction.

E. Grogg is going [i]up[/i] a ramp of θ=π/8 and friction is negligible. He is slowing down.

C. The sled slides forward, but is slowing down with acceleration a=−2gx^ due to friction.

D. Grogg is going down a ramp of θ=π/8 and friction is negligible, so he is accelerating down the incline.

(A) > (B) > (E) = (C) > (D)