In fig. shown, the speed of the truck is v to the right. Find the speed with which the block is moving up at `theta=60^(@)`.

Options

A. v
B. `2v//3`
C. `3v//4`
D. none

Answer

C

Explanation

length of rope =const.
` x+p+2y+sqrt((x-p')^(2)+p^(2))=const`
` (dx)/dt+0+(2dy)/dt+1/2 (sqrt((x-p')^(2)+p^(2))xx2(x-p))(dx)/dt=0`
` v-2v'+cos0v=0`
`2v'=v(1+cos0)`
`v'=v/2(1+cos0)=v/2(1+cos60^(@))`
` v'=(3v)/4 Ans]`