A truck has to move to a dimetrically opposite point on a circular track which surrounds a field. The speed of the truck along the track is `2v_(0)`. While that in the field is `v_(0)`. The driver plans to move along an arc of a circle and then along a straight line as shown.

Options

A. To reach `P` in shortest time, `Q` must be equal to `60^(@)`
B. The minimum time required to rach `P` is `(R )/(v_(0))[(pi)/(6)+sqrt(3)]`
C. The distance travelled to reach `P` in shortest time is `R[(pi)/(3)+sqrt(3)]`.
D. The angle `theta` will not depend on the value of `v_(0)`.

Explanation

`T=(Rtheta)/(2v_(0))+(2Rcos(theta//2))/(v_(0))`
`(dT)/(d theta)=0rArr (R )/(2v_(0))-(Rsin(theta//2))/(v_(0))=0`
`rArr sin(theta//2)=1//2rArrtheta=60^(@)rArrT=(R )/(v_(0))[(pi)/(6)+sqrt(3)]`
Distance `=Rxx(pi)/(3)+2Rxx(sqrt(3))/(2)`