The distance is 17 km
The displacement of the boat is about 12 km at 70° S of W
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Further explanation
Vector is quantity that has magnitude and direction.
One example of a vector is displacement.
Let us now tackle the problem !
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This problem is about Vector Diagram.
On his fishing trip Justin rides in a boat 12 km south.
[tex]d_1 = -12 \widehat{j}[/tex]
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The fish aren’t biting so they go 4 km west.
[tex]d_2 = -4 \widehat{i}[/tex]
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They then follow a school of fish 1 km north.
[tex]d_3 = 1 \widehat{j}[/tex]
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[tex]\texttt{Total Distance} = 12 + 4 + 1 = 17 \texttt{ km}[/tex]
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[tex]d = d_1 + d_2 + d_3[/tex]
[tex]d = -12 \widehat{j} - 4 \widehat{i} + 1 \widehat{j}[/tex]
[tex]d = -4 \widehat{i} - 11 \widehat{j}[/tex]
[tex]\texttt{Total Displacement} = \sqrt{4^2 + 11^2} = \sqrt{137} \approx 12 \texttt{ km}[/tex]
[tex]\texttt{Direction of Displacement} = \theta = \tan^{-1} \frac{11}{4} \approx 70^o \texttt{ south of west}[/tex]
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Learn more
- Direction of Displacement : https://brainly.ph/question/1746541
- Scalar and Vector : https://brainly.ph/question/274572
- Weight : https://brainly.ph/question/545327
- Orientation of Vectors : https://brainly.ph/question/2121753
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Answer details
Grade: High School
Subject: Physics
Chapter: Vectors
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Keywords: Local , Race , Driver , Road , Finish , Line , Displacement , Vector , Degree , North , West , South , Kilometres
