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35. ssm Vector A points along the +y axis and has a magnitude of 100.0 units. Vector B points at an angle of 60.0° above the +x axis and has a magnitude of 200.0 units. Vector C points along the +x axis and has a magnitude of 150.0 units. Which vec- tor has (a) the largest x component and (b) the largest y component?

35. ssm Vector A points along the +y axis and has a magnitude of 100.0 units. Vector B points at an angle of 60.0° above the +x axis and has a magnitude of 200.0 units. Vector C points along the +x axis and has a magnitude of 150.0 units. Which vec- tor has (a) the largest x component and (b) the largest y component?

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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**Problem 35: Vectors and Their Components** Given three vectors: 1. **Vector A**: Points along the \( +y \) axis with a magnitude of 100.0 units. 2. **Vector B**: Points at an angle of \( 60.0^\circ \) above the \( +x \) axis with a magnitude of 200.0 units. 3. **Vector C**: Points along the \( +x \) axis with a magnitude of 150.0 units. **Question**: Which vector has (a) the largest \( x \) component and (b) the largest \( y \) component? **Solution**: 1. **Vector A**: - \( x \)-component: \( 0 \) units - \( y \)-component: \( 100.0 \) units 2. **Vector B**: - \( x \)-component: \( 200.0 \cos 60.0^\circ \) = \( 200.0 \times 0.5 \) = \( 100.0 \) units - \( y \)-component: \( 200.0 \sin 60.0^\circ \) = \( 200.0 \times \frac{\sqrt{3}}{2} \) = \( 200.0 \times 0.866 \) = \( 173.2 \) units 3. **Vector C**: - \( x \)-component: \( 150.0 \) units - \( y \)-component: \( 0 \) units From the above components, we can determine: (a) The vector with the largest \( x \) component is **Vector C** with an \( x \) component of \( 150.0 \) units. (b) The vector with the largest \( y \) component is **Vector B** with a \( y \) component of \( 173.2 \) units.
Transcribed Image Text:**Problem 35: Vectors and Their Components** Given three vectors: 1. **Vector A**: Points along the \( +y \) axis with a magnitude of 100.0 units. 2. **Vector B**: Points at an angle of \( 60.0^\circ \) above the \( +x \) axis with a magnitude of 200.0 units. 3. **Vector C**: Points along the \( +x \) axis with a magnitude of 150.0 units. **Question**: Which vector has (a) the largest \( x \) component and (b) the largest \( y \) component? **Solution**: 1. **Vector A**: - \( x \)-component: \( 0 \) units - \( y \)-component: \( 100.0 \) units 2. **Vector B**: - \( x \)-component: \( 200.0 \cos 60.0^\circ \) = \( 200.0 \times 0.5 \) = \( 100.0 \) units - \( y \)-component: \( 200.0 \sin 60.0^\circ \) = \( 200.0 \times \frac{\sqrt{3}}{2} \) = \( 200.0 \times 0.866 \) = \( 173.2 \) units 3. **Vector C**: - \( x \)-component: \( 150.0 \) units - \( y \)-component: \( 0 \) units From the above components, we can determine: (a) The vector with the largest \( x \) component is **Vector C** with an \( x \) component of \( 150.0 \) units. (b) The vector with the largest \( y \) component is **Vector B** with a \( y \) component of \( 173.2 \) units.
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