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Chapter 3: Q. 42 (page 79)

A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 8.0m/srelative to the air, what direction should they head in order to move directly south?

Short Answer

Expert verified

The correct answer is48.6掳 east of the south

Step by step solution

01

Step 1. Given information

The speed of a duck relative to air is m/s and wind is blowing from the west with a speed of6m/s

02

Step 2. Explanation

As it is given that the speed of a duck relative to air is m/s and the wind is blowing from the west with a speed 6m/s, so the vector diagram will be as follows, where v鈫�wis the velocity of wind, v鈫�dwis the velocity of wind with respect to the wind and vdis the resultant velocity.

Hence, the angle betweenvd鈫�wand vd鈫�,胃, is given as,

sin胃=vwvwd=68胃=48.6掳

Conclusion

The flock of ducks should try to fly in a direction 48.6掳east of the south.

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Most popular questions from this chapter

If C鈫�=A鈫�+B鈫�,Can C=0?Can C<0?For each, show how or explain why not.

FIGURE P3.26shows vectors A鈫�&B鈫�. Find D鈫�=2A鈫�+B鈫�. Write your answer in component form.

7. Draw each of the following vectors. Then find its x - and y- components.

a. v鈫�=7.5m/s,鈥夆赌夆赌�30掳clockwise from the positive x-axis )

b. a鈫�=1.5m/s2,鈥夆赌夆赌�30掳above the negative x-axis )

c. F鈫�=50.0N,鈥夆赌夆赌�36.9掳counter clockwise from the positive y-axis )

A velocity vector 40掳below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component?

5. I A position vector in the first quadrant has an x-component of 6m and a magnitude of 10m . What is the value of its y-component?
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