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Question: 

Determine the speed of the boat with respect to the shore in Example 3-10.

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer: 

$1.41\textrm{ m/s}$

Giancoli 7th Edition, Chapter 3, Problem 40

(1:30)

Chapter 3, Problem 40 is solved.

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Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. The velocity of the boat with respect to the water is 1.85 meters per second and then near the water with respect to the shore going downstream at 1.2 and the example tells us that this angle Θ in order for the boat to go straight across the river and have a velocity with respect to the shore perpendicular to the shore the angle has to be 40.4 degrees and so this is a right triangle and cosine of Θ is the adjacent over the hypotenuse or the boat with respect to the water divided by boat respect to the shore and we can write it as this velocity of the boat with respect to the shore then is velocity of the boat with respect to the water times cos Θ. So that's 1.85 meters per second times cos 40.4 which gives 1.41 meters per second will be the boat's speed with respect to the shore. And so somebody standing on the shore will observe the boat approaching at this speed of 1.41; not at 1.85.