In the arrangement shown in figure (3-Q3), the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed

Let be the length of the string from the mass to the pulley. Let be the length of the string from the mass to the rigid body and be the constant. This is shown in the figure below:

The string through the pulley has velocity along while the mass/string has velocity along .

By Pythagoras theorem in triangle formed in above figure, we have

Differentiating above equation with respect to time, we get

Negative sign is due to the fact that the and decreases as time goes.

Therefore, the equation (1) becomes

The equation above gives the velocity of the mass.