1. The problem statement, all variables and given/known data In hot pursuit, Agent Logan of the FBI must get directly across a 1200-m-wide river in minimum time. The river's current is 0.80 m/s, he can row a boat at 1.60 m/s, and he can run 3.00 m/s. Describe the path he should take(rowing plus running along the shore) for the minimum crossing time, and determine the minimum time. 2. Relevant equations x = v*t 3. The attempt at a solution ---------.------------- 1 2 <---vRiver= 0.80 m/s 0 0 m ---------/---------------- Let the angle between dashes and slash be x. The agent must be at the dot when he's done with rowing and running. The distance between the dot and the point he arrives after rowing(bold dashes) is y. Rowing time is: t1 Running time is: t2 So the equations are: 1200 = 1.60*(sinx)*t1 y = (1.60*(cosx) - 0.80)*t1 y = 3.00 * t2 t1 + t2 = 750/sinx + y/3.00 t1 + t2 = (750/sinx) + (1.60*(cosx) - 0.80)*1200/(3*1.60*(sinx)) In short, t1 + t2 = 550/(sinx) + 400cot(x) After taking derivative, -550(cosx)/(sin2x) - 400/(sin2x) = 0 The angle I got from this is 136.7 degrees. 180-136.7 = 43.3 degrees is the angle between the river current and the boat. But according to my book, the correct answer is the following. "Row at an angle of 24.9 degrees upstream and run 104m along the bank in a total time of 862 seconds." I guess my thinking on this question is wrong. Any ideas how to draw the vectors here?