# Chapter 3 - Kinematics in Two Dimensions; Vectors - Problems: 46

a. 37.5m. b. 75 seconds

#### Work Step by Step

Let the flow of the river be in the x direction and across the river be the y direction. Let S denote Swimmer, R the River, and B the Bank. The pair “SB”, for example, represents the swimmer’s motion relative to the bank. $$\vec{v_{SB}} = \vec{v_{SR}} + \vec{v_{RB}}$$ $$= (0, 0.60 m/s) + (0.50 m/s, 0)$$ $$= (0.50 m/s, 0.60 m/s)$$ $$\vec{v_{SB}} = (0.50 m/s, 0.60 m/s)$$ a. Find the downstream distance from analyzing the x-direction. (0.50 m/s)(75 s) = 37.5 m. b. Find the time to cross from analyzing the y-direction: t = (45 m)/(0.60 m/s) = 75 seconds.

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