A man is on straight road AC, standing at A. He wants to get to a point P which is in field at a distance ‘d’ off the road (see figure). Distance AB is `l = 50`. The man can run on the road at a speed `v_(1) = 5 m//s` and his speed in the field is `v_(2) = 3 m//s`.
(a) Find the minimum value of ‘d’ for which man can reach point P in least possible time by travelling only in the field along the straight line AP.
(b) If value of ‘d’ is half the value found in (a), what length the man must run on the road before entering the field, in order to reach ‘P’ in least possible time.
