ch04-p089 - 89. We establish coordinates with i pointing to...

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(b) Using the result from part (a), we find v bg = v bw cos θ = 5.5 km/h. Thus, traveling a distance of A = 6.4 km requires a time of (6.4 km)/(5.5 km/h) = 1.15 h or 69 min. (c) If her motion is completely along the y axis (as the problem implies) then with v wg = 3.2 km/h (the water speed) we have total = + = 1.33 h + bw wg bw wg DD t vv v v where D = 3.2 km. This is equivalent to 80 min. (d) Since + bw wg bw wg bw wg bw wg D D v v v v += + −− + the answer is the same as in the previous part, i.e., total = 80 min t . (e) The shortest-time path should have 0. This can also be shown by noting that the case of general leads to ˆˆ cos i ( sin + ) j bg bw wg bw bw wg vvvv v v θθ =+= + GGG where the x component of G v bg must equal l / t . Thus, = cos bw l t v which can be minimized using dt / d = 0. (f) The above expression leads to t = (6.4 km)/(6.4 km/h) = 1.0 h, or 60 min. 89. We establish coordinates with
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