原题.一只狼沿半径为R的圆形岛边缘沿逆时针方向以速度v_1匀速跑动,如图1所示,狼过A点时,一只猎犬以匀速率v_2从O点出发追击狼,若追击过程中狼、猎犬、O点始终在一条直线上,则猎犬是沿着什么轨迹运动的?能否追上狼?如果能,则所用的时间是多少?解析:如图2所示,狼某时刻运动到B点,此时猎犬的极径为r,极角为θ,其速度v_2可以正交分解为径向速度v_(2r)和角向速度v_(2θ), The original title. A wolf along the edge of a circular island radius R at a uniform speed counterclockwise v_1 running at uniform speed, as shown in Figure 1, wolf A point, a hound at a uniform rate v_2 chase from O point Wolf, if the pursuit of wolves, hounds, O point is always in a straight line, the hound is along what trajectory? Can catch up with the wolf? If so, what time is? Analysis: As shown in Figure 2 The wolf at some point moves to point B, at this time the radius of the hound is r, the polar angle is θ, and its velocity v_2 can be decomposed orthogonally into radial velocity v_ (2r) and angular velocity v_ (2θ)