A lift goes up with 10 m/s. a pulley P is fixed to the ceiling of the lift. To this pulley other two pulley `P_(1)` and `P_(2)` are attached. `P_(1)` moves up with velocity 30 m/s. A moves up with velocity 10 m/s. D is moving downwards with velocity 10 m/s at same instant of time. Find the velocity of B and that of C at that instant. Assume that all velocities are relative to the ground.

Answer

5

Explanation

Apply constraint on pulley `P`
`vecv_(p_(1)//p)=-vecv_(p_(2)//p)),vecv_(p_(1))-vecv_(p)=-(vecv_(p_(2))-vecv_(p))`
`vecv_(p_(1)),vecv_(p),vecv_(p_(2))` are respective velocity w.r.t ground
`vecv_(p_(2))=2vecv_(p)-vecv_(p_(1)),=2[10hatj]-[-30hatj]=-10hatj`
Now apply constraint eqn on pulley `P_(2)`
`vecvc-vecv_(p_(2))=-(vecvp-vp_(2))`
`vecvc=2vecv_(p_(2))-vecv_(D)=2[-10hatj]-[-10hatj]vecv_(C)=10hatj`
Apply constraint eqn on pulley `P_(1)` to get
`vecv_(A)-vecv_(p_(1))=-(vecv_(B)-vecv_(p_(1))),vecv_(B)=2vecv_(p_(1))-vecv_(A)`
`=2[30hatj]-[10hatj]=50hatj` .