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In the instant shown in the diagram the ...

In the instant shown in the diagram the board is moving up (vertically) with velocity `v`. The drum winds up at a constant rate `omega`. If the radius of the drum is `R` and the board always remains horizontal, find the value of velocity in terms of `R, theta, omega`.

Text Solution

Verified by Experts

The correct Answer is:
`(omegaR)/(1+costheta)`
`I=y+z` (total length at any time) `=y+sqrt(y^(2)+l_(1)^(2))`
`(dl)/(dt)=(dy)/(dt)+y/(sqrt(y^(2)+l_(1)^(2)))(dy)/(dt)`
`omega R=v(1+costheta), v=(omegaR)/(1+costheta)`
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