Question

Lucas rows at a constant speed of 1.2 m/s in still water. He wants to row directly across a lazy river to get to his brother Jack. The stream is shown to the right. of the current direcion a. 6ps At what angle upstream from directly across the river should Lucas head if the current of the river is 0.3 m/s? Include a clearly labeled figure. Give your answer in degrees, rounded to 2 decimal places. b. 3ps If the river is 300 meters wide, how long will it take Lucas to get Jack? Round to I decimal place

Answer 1

The resultant velocity of v_2 (velocity of Lucas) and v_s (velocity of steam) in the velocity that Lucas will actually follow angle between v_L & v_s = (90 - theta) sin theta = Vertical-bar v_s Vertical-bar / Vertical-bar v_L Vertical-bar = 0.3/1.2 = 0.25 implies theta = sin^-1 (0.25) = 14.48 degree rightarrow Ans (a) v_r = squareroot v_s^2 + v_L^2 + 2 v_s v_L cos (p0 - theta) v_r = squareroot (0.3)^2 + (1.2)^2 + 2 times 0.3 times 1.2 times 0.25 = 1.3077 m/s If river is 300 m wide time taken = 300/ 1.3077 s = 229.4 seconds rightarrow Ans (b)