# Chapter 3 - Kinematics in Two Dimensions; Vectors - Problems: 39

1.66m/s, 25$^o$ relative to the river.

#### Work Step by Step

Let the flow of the river be in the x direction and "across the river" be in the y direction. Let H denote Huck, R the raft, and B the Bank. The pair “HB”, for example, represents Huck’s motion relative to the Bank. $$\vec{v_{HB}} = \vec{v_{HR}} + \vec{v_{RB}}$$ $$= (0, 0.70 m/s) + (1.50 m/s, 0) = (1.50 m/s, 0.70 m/s)$$ $$\vec{v_{HB}} = (1.50 m/s, 0.70 m/s)$$ Find the magnitude using the Pythagorean Theorem and the direction using the definition of the tangent. $$v_{HB} = 1.66 m/s.$$ The angle is at 25$^o$ relative to the river.

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