Question

On his fishing trip Justin rides in a boat 12 km south The fish aren’t biting so they go 4 km west. They then follow a school of fish 1 km north. What distance did they cover? What was their displacement?

Answer 1

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.

$d_1 = -12 \widehat{j}$

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The fish aren’t biting so they go 4 km west.

$d_2 = -4 \widehat{i}$

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They then follow a school of fish 1 km north.

$d_3 = 1 \widehat{j}$

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$\texttt{Total Distance} = 12 + 4 + 1 = 17 \texttt{ km}$

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$d = d_1 + d_2 + d_3$

$d = -12 \widehat{j} - 4 \widehat{i} + 1 \widehat{j}$

$d = -4 \widehat{i} - 11 \widehat{j}$

$\texttt{Total Displacement} = \sqrt{4^2 + 11^2} = \sqrt{137} \approx 12 \texttt{ km}$

$\texttt{Direction of Displacement} = \theta = \tan^{-1} \frac{11}{4} \approx 70^o \texttt{ south of west}$

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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

Answer 2

In finding the distance that covers we simply add the three km which is 
12 + 4 + 1 = 17km

17 km is the distance they cover.

We are going to use the displacement formula which is
d = vt + 1/2 at^2
d = 11.7 km

11.7 is the displacement