GOAL Solve a complex two- dimensional relative motion problem. PROBLEM If the sk
ID: 1586571 • Letter: G
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GOAL Solve a complex two- dimensional relative motion problem. PROBLEM If the skipper of the boat moves with the speed of 10.0 km/h relative to the water and wants to travel due north (along the BE direction), as in Figure (a), in what direction should he head? What is the speed of the boat, according to an observer on the shore? The river is flowing east at 5.00 km/h. STRATEGY In this situation, we must find the heading of the boat and its velocity with respect to the water, using the fact that the boat travels due north. SOLUTION Arrange the bhree quantities Organize a table of velocity Vector -component -(10.0 km/h) sn (10..0 ) cos @ -(100 m/s) sn-5.00 km The s-component of the relative velocity equation can be used to find m2.00 Apply the inverse sine Mandon and find 6, which is the beat's heading, east of 0-sn'l(20).30 velocity equation can be used to find LEARN MORE REMARKS From the figure, we see that this problem can be solved with the Pythagorean theorem, Because the problem involves a right triangle: the boat's x-component of velocity exactly cancels the river's velocity. When this is not the case, a more general technique is necessary, as shown in the following exercise. Notice that in the x-component of the relative velocity equation a minus sign had to be included in the termm -(10.0 km/h)sin because the x-component of the boat's velocity with respect to the river is negative. QUESTION If the boat is instead heading due north relative to the water (instead of relative to the shore) while having the same speed relative to the water as the example above (see the figure below), then the angle in the two image will not be the same. What has changed? (Select all that apply.)Explanation / Answer
The magnitude of the boat velocity is different
THe velocity of the boat is now the hypotenuse of the triangle shown in diagram
The component of boat velocity across river is larger (because the boat is headed directly across the river)
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