A square plate of mass `10 kg` and side `20 m` is moving along the groove with the help of two ideal roller (massless), connected at the corners `A` and `B` of the square as shown in the figure. At the given instant of time during motion (as shown in the figure), the corner `A` is moving with velocity `16 m//s` downward. Find the speed of corner `D`(approximately).

Options

A. `32.5 m//s`
B. `16.5 m//s`
C. `8.5 m//s`
D. none

Explanation

`cos37^(@)=x//arArrx=4a//5=16mrArromega=1rad//s`.
`cos53^(@)=(a^(2)+x^(2)-y^(2))/(2ax)`
`rArr a^(2)+x^(2)-y^(2)=384`
`rArry^(2)=400+256-384=272`
`y=16.5m` (approximately)
`v_(D)=yomega=16.5m//s`