Question

10) A kayaker can paddle at 2 m/s. She wants to cross a 50 m wide river that is flowing at 0.75 m/s. If she points her kayak straight across and moves 2 m/s relative to the water, what a. is her net velocity vector relative to the shore? How far downstream will she be when she reaches the other side? She wants to paddle straight across. What angle upstream should she point the b. c. kayak and how long will this trip take?

Answer 1

" Velocity of Kayaker = V_b = 2m/s Width = W = 50cm Velocity of river = V_r = 0.75 m/s Now, when Kayaker moves in river it has resultant velocity, given by V_R = squareroot V^2_k + V^2_r = squareroot 4 + 0.5625 = squareroot 4.5625 V_R = 2.136m/s this will be the resultant velocity of the Kayaker in river. \r\n (b) Kayaker will be at point �B"" down the stream. Now to find AB, consider vector Delta ABC tan theta = V_r/V_k = AB/AC Therefore AB = V_r/V_k times A_c = 0.75/2 times 50 cm AB = 18.75 cm Therefore she will go down stream by 18.75 cm (c) For kayaker to cross straight she must have resultant velocity along CB as shown. \r\n again, in Delta ABC sin theta = V_r/V_b = 0.75/2 = 0.375 theta = sin^-1 (0.375) theta = 22.02 degree she has to go 22.02 degree upstream to reach a point straight. Now,"