Find acceleration and velocity of a body:

A rope of length L connects through the wheel A & the weight B by passing over a pulley of negligible size at C as illustrated in Figure. At the point when x = 9 m an acceleration of A is equivalent to 1 m/s² & velocity is 3 m/s both rightward. Find acceleration and velocity of B.

Solution

Assume AC be equivalent to z

∴          BC = L - z

Therefore

 y = h - (L - z)

 Take differentiation with respect to t it becomes

Also,

Also,

             z ²  = h²  + x²

Thus, by taking differentiation, it becomes following

or         z V_B  = x V_A

Again differentiation results

or         z a_B  + V ₂  = x a_A  + V ₂

While   x = 9 m & h = 12 m, z = 15 m

15 V = 9 × 3 or V = 9 × 3 = 1.8 m/s

Also

 15 a_B  + (1.8)²  = 9 × 1 + 3²

 or