Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Question
Chapter 3, Problem 41P
To determine
The single displacement that will take the bear back to the cave.
Expert Solution & Answer
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) An object follows as shown below. What is the displacement from the last point to the starting point? Express your answer (a) in unit vector notation, and (b) as a magnitude and direction.
Problem
An explorer in Antarctica leaves his shelter during a whiteout. He takes 50 m northeast, next 180 m at 72° north of west, and then
150 m due south. Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the
method of components, that will return him to his shelter.
Solution
By vector-component approach, we list down the given in a table as follows:
Given
x-component (w/ sign direction)
y-component (w/ sign direction)
A = 50 m NE
m
m
B = 180 m 72° NW
m
C = 150 m s
m
Resultant
m
m
Thus, the magnitude of the resultant vector is
R =
With a direction of
e =
O NW
Therefore, the vector needed for him to successfully get back home is
Rhome =
SE
m
Problem
An explorer in Antarctica leaves his shelter during a whiteout. He takes 50 m northeast, next 180 m at 72° north of west, and then
150 m due south. Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the method
of components, that will return him to his shelter.
Solution
By vector-component approach, we list down the given in a table as follows:
Given
x-component (w/ sign direction)
y-component (w/ sign direction)
A = 50 m NE
m
B = 180 m 72° NW
m
m
C= 150 m S
m
m
Resultant
m
Thus, the magnitude of the resultant vector is
R =
m
With a direction of
O NW
Therefore, the vector needed for him to successfully get back home
Rhome
O SE
%3!
E E EE
E E EE
Chapter 3 Solutions
Physics for Scientists and Engineers, Vol. 1
Ch. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10P
Ch. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 51PCh. 3 - Prob. 52PCh. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Prob. 55PCh. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Prob. 60PCh. 3 - Prob. 61PCh. 3 - Prob. 62PCh. 3 - Prob. 63PCh. 3 - Prob. 64PCh. 3 - Prob. 65PCh. 3 - Prob. 66PCh. 3 - Prob. 67PCh. 3 - Prob. 68PCh. 3 - Prob. 69PCh. 3 - Prob. 70PCh. 3 - Prob. 71PCh. 3 - Prob. 72PCh. 3 - Prob. 73PCh. 3 - Prob. 74PCh. 3 - Prob. 75PCh. 3 - Prob. 76PCh. 3 - Prob. 77PCh. 3 - Prob. 78PCh. 3 - Prob. 79PCh. 3 - Prob. 80PCh. 3 - Prob. 81PCh. 3 - Prob. 82PCh. 3 - Prob. 83PCh. 3 - Prob. 84PCh. 3 - Prob. 85PCh. 3 - Prob. 86PCh. 3 - Prob. 87PCh. 3 - Prob. 88PCh. 3 - Prob. 89PCh. 3 - Prob. 90PCh. 3 - Prob. 91PCh. 3 - Prob. 92PCh. 3 - Prob. 93PCh. 3 - Prob. 94PCh. 3 - Prob. 95PCh. 3 - Prob. 96PCh. 3 - Prob. 97PCh. 3 - Prob. 98PCh. 3 - Prob. 99PCh. 3 - Prob. 100PCh. 3 - Prob. 101PCh. 3 - Prob. 102PCh. 3 - Prob. 103PCh. 3 - Prob. 104PCh. 3 - Prob. 105PCh. 3 - Prob. 106PCh. 3 - Prob. 107PCh. 3 - Prob. 108PCh. 3 - Prob. 109PCh. 3 - Prob. 110PCh. 3 - Prob. 111PCh. 3 - Prob. 112PCh. 3 - Prob. 113PCh. 3 - Prob. 114PCh. 3 - Prob. 115PCh. 3 - Prob. 116PCh. 3 - Prob. 117PCh. 3 - Prob. 118PCh. 3 - Prob. 119PCh. 3 - Prob. 120PCh. 3 - Prob. 121PCh. 3 - Prob. 122P
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- Problem An explorer in Antarctica leaves his shelter during a whiteout. He takes 50 m northeast, next 180 m at 72° north of west, and then 150 m due south. Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the method of components, that will return him to his shelter. Solution By vector-component approach, we list down the given in a table as follows: Given X-component (w/ sign direction) y-component (w/ sign direction) A = 50 m NE m m B = 180 m 72° NW m m C = 150 m s m m Resultant m m Thus, the magnitude of the resultant vector is R= m With a direction of o = ONW Therefore, the vector needed for him to successfully get back home is Rhome = O SE marrow_forwardProblem An explorer in Antarctica leaves his shelter during a whiteout. He takes 50 m northeast, next 180 m at 72° north of west, and then 150 m due south. Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the method of components, that will return him to his shelter. Solution By vector-component approach, we list down the given in a table as follows: Given x-component (w/ sign direction) -component (w/ sign direction) A = 50 m NE B = 180 m 72° NW m m C = 150 m S m m Resultant Thus, the magnitude of the resultant vector is R = With a direction of O NW Therefore, the vector needed for him to successfully get back home is Rhome = SE marrow_forwardA woman enters a store and walks north a distance of 150 m and then turns East by 150 degrees before walking another 50 m. What is the woman's displacement from when she first entered the store?arrow_forward
- Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. One goose is flying at 100 km/h relative to the air but a 42 km/h wind is blowing from west to east. a) At what angle relative to the north-south direction should this bird head to travel directly southward relative to the ground? b) How long will it take the goose to cover a ground distance of 550 km from north to south? (Note: Even on cloudy nights, many birds can navigate using the earth's magnetic field to fix the north-south direction.)arrow_forwardA truck travels due east for a distance of 1.7 km, turns around and goes due west for 7.5 km, and finally turns around again and travels 2.5 km due east. (a) What is the total distance that the truck travels? (b) What are the magnitude and direction of the truck's displacement?arrow_forwardProblem An explorer in Antarctica leaves his shelter during a whiteout. He takes 50 m northeast, next 180 m at 72° north of west, and then 150 m due south. Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the method of components, that will return him to his shelter. Solution By vector-component approach, we list down the given in a table as follows: x-component (w/ sign direction) y-component (w/ sign direction) Given A = 50 m NE m B = 180 m 72° NW m C = 150 m S m m Resultant m Thus, the magnitude of the resultant vector is R = With a direction of e = O NW Therefore, the vector needed for him to successfully get back home is Rhome = OSE m EEarrow_forward
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