In Fig., pulley P moves to the right with a constant speed u. The downward speed of A is 
, and the speed of B to the right is 
,
Text Solution
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(b, d): At any instant of time, let the length of the string BP = l 1 and the length PA = l 2 . In a further time t, let B move to the right by x and A move down by y, while P moves to the right by ut. As the length of the string must remain constant,
l 1 + l 2 = (l 1 – x + ut) + (l 2 + y)
or x = ut + y
or 
= u + 
= speed of B to the right = v B , 
= downward speed of A = v A .
∴ ∴ v B = u + v A Also, 
B = 
A
or a B = a A .
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