As shown in figure `AB` represents an infinite wall tangential to a horizontal semi circular track.`O` is a point source of light on the ground at the centre of the circle. A block moves along the circular track with speed `v` starting from the point where the wall touches the circle. If the velocity and acceleration of shadow along the length of the wall is respectively `'V'` and `'a'` then,

Options

A. `V=v cos"(vt)/R`
B. `V=v sec^(2)((vt)/R)`
C. `a=v^(2)/Rsec^(2)((vt)/R)tan((vt)/R)`
D. `a=(2v^(2))/Rsec^(2)((vt)/R)tan((vt)/R)`

Answer

B, D

Explanation

`"T"an theta=y/R,y=R tan theta`
`v=(dy)/(dt)=R sec^(2)theta(("d"theta)/(dt))=Romegasec^(2)theta`
`= v sec^(2)((vt)/R)`
acceleration of the shadow:
`a=(dv)/(dt)=(2v^(2))/Rsec^(2)((vt)/R)tan((vt)/R)`