Related Rates of Accelerations in Pulley Problem

[Alexanddros81]

Homework Statement

Hi!
I am new to this forum and i have problem understanding sample problem 13.5 from Vector Mechanics for Engineers 10th edition Statics and dynamics. (Beer)
In particular I don't understant in part b how he comes to the assumption a_C=-1/2a_D

If anyone can help
thanks

Homework Equations

Uniform motion: ∑F_y=0
Accelerated Motion: ∑F_y=ma

The Attempt at a Solution

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[Doc Al]

In particular I don't understant in part b how he comes to the assumption a_C=-1/2a_D

If D raises by one unit of distance, by how many units must C lower? (Take a piece of string and play with it.)