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Taking a Hike A hiker begins a trip by first walking 19.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 44.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower. W-OE y (km) Tower R B -x (km) Car 45.0° 60.0° Tent (a) Determine the components of the hiker's displacement for each day. SOLUTION Conceptualize We conceptualize the problem by drawing a sketch as in the figure. If we denote the displacement vectors on the first and second days by A and B, respectively, and use the -Select---v as the origin of coordinates, we obtain the vectors shown in the figure. The sketch allows us to estimate the resultant vector as shown. Categorize Drawing the resultant R, we can now categorize this problem as one we've solved before:-Select- already solved if we are careful to conceptualize them. Once we have drawn the displacement vectors änd categorized the problem, this problem is no longer about a hiker, a walk, a car, a tent, or a tower. It is a problem about vector addition, one that we have already solved. v of two vectors. You should now have a hint of the power of categorization in that many new problems are very similar to problems we have Analyze Displacement A has a magnitude of km and is directed • below positive x-axis. Find the components (in km) of A using these equations: A A cos(-45.0°) - km A, A sin(-45.0°) - The -Select- V value of A, indicates the hiker walks in the -Select-v y-direction on the first day. The signs of A, and A, also are evident from the figure. Find the components (in km) of B using these equations: B.- B cos(60.0°) - km

Taking a Hike A hiker begins a trip by first walking 19.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 44.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower. W-OE y (km) Tower R B -x (km) Car 45.0° 60.0° Tent (a) Determine the components of the hiker's displacement for each day. SOLUTION Conceptualize We conceptualize the problem by drawing a sketch as in the figure. If we denote the displacement vectors on the first and second days by A and B, respectively, and use the -Select---v as the origin of coordinates, we obtain the vectors shown in the figure. The sketch allows us to estimate the resultant vector as shown. Categorize Drawing the resultant R, we can now categorize this problem as one we've solved before:-Select- already solved if we are careful to conceptualize them. Once we have drawn the displacement vectors änd categorized the problem, this problem is no longer about a hiker, a walk, a car, a tent, or a tower. It is a problem about vector addition, one that we have already solved. v of two vectors. You should now have a hint of the power of categorization in that many new problems are very similar to problems we have Analyze Displacement A has a magnitude of km and is directed • below positive x-axis. Find the components (in km) of A using these equations: A A cos(-45.0°) - km A, A sin(-45.0°) - The -Select- V value of A, indicates the hiker walks in the -Select-v y-direction on the first day. The signs of A, and A, also are evident from the figure. Find the components (in km) of B using these equations: B.- B cos(60.0°) - km

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 33P: A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following...
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(b) Determine the components of the hiker's resultant displacement R for the trip. Find an expression for R in terms of unit vectors. SOLUTION Use the following equation to find the components (in km) of the resultant displacement R = A + B: Ry = A, + B, = km R, = A, + B,- km Write the total displacement (in km) in unit-vector form: R j) km Finalize Looking at the graphical representation in the figure, both components of R are positive, putting the final position in the -Select-- v quadrant of the coordinate system. Is this consistent with your answer? EXERCISE A dolphin swims due east for 1.60 km, then swims 7.00 km in the direction south of west. What are the magnitude and direction of the vector that will take the dolphin back to its starting point? (Enter the magnitude in km and the direction in degrees north east.) Hint magnitude km direction ° north of east
Transcribed Image Text:(b) Determine the components of the hiker's resultant displacement R for the trip. Find an expression for R in terms of unit vectors. SOLUTION Use the following equation to find the components (in km) of the resultant displacement R = A + B: Ry = A, + B, = km R, = A, + B,- km Write the total displacement (in km) in unit-vector form: R j) km Finalize Looking at the graphical representation in the figure, both components of R are positive, putting the final position in the -Select-- v quadrant of the coordinate system. Is this consistent with your answer? EXERCISE A dolphin swims due east for 1.60 km, then swims 7.00 km in the direction south of west. What are the magnitude and direction of the vector that will take the dolphin back to its starting point? (Enter the magnitude in km and the direction in degrees north east.) Hint magnitude km direction ° north of east
Taking a Hike A hiker begins a trip by first walking 19.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 44.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower. w-OE y (km) Tower B x (km) Can 45.0° 60.0° (a) Determine the components of the hiker's displacement for each day. SOLUTION Conceptualize We conceptualize the problem by drawing a sketch as in the figure. If we denote the displacement vectors on the first and second days by A and B, respectively, and use the -Select--v as the origin of coordinates, we obtain the vectors shown in the figure. The sketch allows us to estimate the resultant vector as shown. Categorize Drawing the resultant R, we can now categorize this problem as one we've solved before:-Select- already solved if we are careful to conceptualize them. Once we have drawn the displacement vectors änd categorized the problem, this problem is no longer about a hiker, a walk, a car, a tent, or a tower. It is a problem about vector addition, one that we have already solved. v of two vectors. You should now have a hint of the power of categorization in that many new problems are very similar to problems we have Analyze Displacement A has a magnitude of km and is directed • below positive x-axis. Find the components (in km) of A using these equations: A A cos(-45.0°) - km A, A sin(-45.0°) - The -Select-- v value of A, indicates the hiker walks in the -Select--v y-direction on the first day. The signs of A, and A, also are evident from the figure. Find the components (in km) of B using these equations: B,- B cos(60.0°) - B, - B sin(60.0°)- km km
Transcribed Image Text:Taking a Hike A hiker begins a trip by first walking 19.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 44.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower. w-OE y (km) Tower B x (km) Can 45.0° 60.0° (a) Determine the components of the hiker's displacement for each day. SOLUTION Conceptualize We conceptualize the problem by drawing a sketch as in the figure. If we denote the displacement vectors on the first and second days by A and B, respectively, and use the -Select--v as the origin of coordinates, we obtain the vectors shown in the figure. The sketch allows us to estimate the resultant vector as shown. Categorize Drawing the resultant R, we can now categorize this problem as one we've solved before:-Select- already solved if we are careful to conceptualize them. Once we have drawn the displacement vectors änd categorized the problem, this problem is no longer about a hiker, a walk, a car, a tent, or a tower. It is a problem about vector addition, one that we have already solved. v of two vectors. You should now have a hint of the power of categorization in that many new problems are very similar to problems we have Analyze Displacement A has a magnitude of km and is directed • below positive x-axis. Find the components (in km) of A using these equations: A A cos(-45.0°) - km A, A sin(-45.0°) - The -Select-- v value of A, indicates the hiker walks in the -Select--v y-direction on the first day. The signs of A, and A, also are evident from the figure. Find the components (in km) of B using these equations: B,- B cos(60.0°) - B, - B sin(60.0°)- km km
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