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LEARN M ORE 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 term -(10.0 km/h)sin 0 because the x-component of the boat's velocity with respect to the river is negative. If the boat is instead heading due north relative to the water (instead of relative to the QUESTION shore) while having the same speed relative to the water as the example above (see the figure below), then the angle 0 in the two image will not be the same. What has changed? (Select all that apply.) FRE BE BR W- The velocity of the boat is now the hypotenuse of the triangle shown in the diagram. The component of the boat velocity across the river is smaller. The magnitude of the boat velocity is different. The component of the boat velocity across the river is larger. The velocity of the boat is now the base of the triangle shown in the diagram. PRACTICE IT Use the worked example above to help you solve this problem. If the skipper of a boat moves with a speed of 16.4 km/h relative to the water and wants to travel due north, as shown 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 4.10 km/h. speed km/h ° east of north direction EXERCISE HINTS: GETTING STARTED I'M STUCK! Suppose the river is moving east at 3.40 km/h and the boat is traveling 45.0° south of east with respect to Earth. If the boat's heading in the water is 60.0° south of east, find the following. (See Figure (b).) (a) the speed of the boat with respect to the Earth km/h (b) the speed of the boat with respect to the river km/h Need Help? Read It

LEARN M ORE 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 term -(10.0 km/h)sin 0 because the x-component of the boat's velocity with respect to the river is negative. If the boat is instead heading due north relative to the water (instead of relative to the QUESTION shore) while having the same speed relative to the water as the example above (see the figure below), then the angle 0 in the two image will not be the same. What has changed? (Select all that apply.) FRE BE BR W- The velocity of the boat is now the hypotenuse of the triangle shown in the diagram. The component of the boat velocity across the river is smaller. The magnitude of the boat velocity is different. The component of the boat velocity across the river is larger. The velocity of the boat is now the base of the triangle shown in the diagram. PRACTICE IT Use the worked example above to help you solve this problem. If the skipper of a boat moves with a speed of 16.4 km/h relative to the water and wants to travel due north, as shown 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 4.10 km/h. speed km/h ° east of north direction EXERCISE HINTS: GETTING STARTED I'M STUCK! Suppose the river is moving east at 3.40 km/h and the boat is traveling 45.0° south of east with respect to Earth. If the boat's heading in the water is 60.0° south of east, find the following. (See Figure (b).) (a) the speed of the boat with respect to the Earth km/h (b) the speed of the boat with respect to the river km/h Need Help? Read It

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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LEARN M ORE 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 term -(10.0 km/h)sin 0 because the x-component of the boat's velocity with respect to the river is negative. If the boat is instead heading due north relative to the water (instead of relative to the QUESTION shore) while having the same speed relative to the water as the example above (see the figure below), then the angle 0 in the two image will not be the same. What has changed? (Select all that apply.) FRE BE BR W- The velocity of the boat is now the hypotenuse of the triangle shown in the diagram. The component of the boat velocity across the river is smaller. The magnitude of the boat velocity is different. The component of the boat velocity across the river is larger. The velocity of the boat is now the base of the triangle shown in the diagram.
Transcribed Image Text:LEARN M ORE 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 term -(10.0 km/h)sin 0 because the x-component of the boat's velocity with respect to the river is negative. If the boat is instead heading due north relative to the water (instead of relative to the QUESTION shore) while having the same speed relative to the water as the example above (see the figure below), then the angle 0 in the two image will not be the same. What has changed? (Select all that apply.) FRE BE BR W- The velocity of the boat is now the hypotenuse of the triangle shown in the diagram. The component of the boat velocity across the river is smaller. The magnitude of the boat velocity is different. The component of the boat velocity across the river is larger. The velocity of the boat is now the base of the triangle shown in the diagram.
PRACTICE IT Use the worked example above to help you solve this problem. If the skipper of a boat moves with a speed of 16.4 km/h relative to the water and wants to travel due north, as shown 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 4.10 km/h. speed km/h ° east of north direction EXERCISE HINTS: GETTING STARTED I'M STUCK! Suppose the river is moving east at 3.40 km/h and the boat is traveling 45.0° south of east with respect to Earth. If the boat's heading in the water is 60.0° south of east, find the following. (See Figure (b).) (a) the speed of the boat with respect to the Earth km/h (b) the speed of the boat with respect to the river km/h Need Help? Read It
Transcribed Image Text:PRACTICE IT Use the worked example above to help you solve this problem. If the skipper of a boat moves with a speed of 16.4 km/h relative to the water and wants to travel due north, as shown 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 4.10 km/h. speed km/h ° east of north direction EXERCISE HINTS: GETTING STARTED I'M STUCK! Suppose the river is moving east at 3.40 km/h and the boat is traveling 45.0° south of east with respect to Earth. If the boat's heading in the water is 60.0° south of east, find the following. (See Figure (b).) (a) the speed of the boat with respect to the Earth km/h (b) the speed of the boat with respect to the river km/h Need Help? Read It
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