Find out the velocity of block E as shown in figure.

Explanation

We first choose the longest string in which point j (block E) lie. (abcdefghij)

Step 2 : Now write equation according to the velocity of each point (either increase or decrease the length) `v_a + v_b + v_c + v_d + v_e + v_f + v_g + v_h + v_i + v_j= 0" "`...(1)
Now find value of `v_a, v_b` ..... in a following way
`v_k (v_A + v_B)/(2)" "` (from second format) `= (8- 2)/2 = 3 m//"sec"`. (upward)
`v_a = (v_K + v_C)/2` (from 2nd format)
`=(3 + 2)/2 = 5//2 m//"sec"` (upward)
`v_(x) = 4m//s` (from first format of constrain)
from 2nd format of constrain `v_x = (v_y + v_z)/(2)`
`:. v_x) = 0` (fixed)
`implies v_(y) = 2v_(x) = 8m//s`(upward)
`implies` Now `v_a = – 5/2 m//s` (decreases the length)
`v_b = v_c = v_d = v_e = 0` (attached to fixed object)
`v_f = v_g = 1m//s` (increases the length)
`v_h = v_i = v_y = 8 m/s` (increase the length)
Let us assume block E move upward then `v_j = - v_E`
(decrease the length) Puting the above values in eq. (1)
`implies -5/2 + 1 + 1 + 8 + 8 -v_E = 0`
`v_E = 31//2 m//s` (upward)