In pursuit of both adventure and treasure, the pirate Jack Sparrow sails his ship on the open ocean. The ship starts out at the coordinates x = + 400 km, y = - 200 km, as shown in the figure. First it undergoes a displacement D, = - 600 km i + 300 km j, traveling a distance of 1000 km in 100 hours. Next it undergoes a displacement D, = + 300 km i - 200 km j, traveling a distance of 500 km in 90 hours. Then it stops for 10 hours. Finally, it undergoes a displacement D, with scalar components D,, = - 500 km, D,, 100 km while moving a distance of 600 km in 100 hours. 1+y (km) 300 200 100 +x (km) -400 - 300 200 100 100 200 300 400 -100 -200 +-300 11. At the end of the entire journey described above, the ship is located at coordinates A. x= - 400 km, y = - 200 km. B. x = - 200 km, y = - 400 km. C. x= - 800 km, y = - 200 km. D. x = - 800 km, y = 0 km. E. x= 400 km, y = - 200 km. 12. At the end of the entire journey described above, the ship has traveled a total distance of A. 2100 km in the negative x direction. B. 2100 km. C. - 2100 km. E. - 800 km i. D. 800 km. 13. The ship's average speed (for the entire journey described above) is A. - 2.67 km/hour. B. 2.67 km/hour. C. - 7.00 km/hour. D. - 7.00 km/hour E. 7.00 km/hour. 14. The ship's overall displacement (for the entire journey described above) equals A. - 800 km. B. 800 km. C. 2100 km in the negative x direction. D. - 800 km i. E. 2100 km. 15. For the entire journey described above, the ship's average velocity is A. - 7.00 km/hour i. 8. 7.00 km/hour i. C. - 2.67 km/hour i. D. 2.67 km/hour. E. 7.00 km/hour.

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Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Question

In pursuit of both adventure.and treasure, the pirate Jack Sparrow sails his ship on the open ocean.
The ship starts out at the coordinates x = + 400 km, y = - 200 km, as shown in the figure.
First it undergoes a displacement D,=-600 kmi + 300 km j , traveling a distance of 1000 km in 100 hours.
Next it undergoes a displacement D,
= + 300 km i- 200 km j , traveling a distance of 500 km in 90 hours.
Then it stops for 10 hours.
Finally, it undergoes a displacement D, with scalar components D
- 500 km, Dzy
= - 100 km while
%3D
moving a distance of 600 km in 100 hours.
1+y (km)
300
200
100
+x (km)
400 -300
- 200 - 100
100
200
300
400
-100
-200
300
11. At the end of the entire journey described above, the ship is located at coordinates
A. x = - 400 km, y = - 200 km.
B. x = - 200 km, y = - 400 km.
C. x = - 800 km, y = - 200 km.
D. x = - 800 km, y = 0 km.
E. x = 400 km, y = - 200 km.
12. At the end of the entire journey described above, the ship has traveled a total distance of
A. 2100 km in the negative x direction.
В. 2100 km.
C. - 2100 km.
D. 800 km.
E. -800 km î .
13. The ship's average speed (for the entire journey described above) is
A. - 2.67 km/hour.
B. 2.67 km/hour.
C. -7.00 km/hour.
D. -7.00 km/hour
E. 7.00 km/hour.
14. The ship 's overall displacement (for the entire journey described above) equals
A. 800 km.
B. 800 km.
C. 2100 km in the negative x direction.
D. -800 km î.
E. 2100 km.
15. For the entire journey described above, the ship's average velocity is
A. -7.00 km/hour i.
B. 7.00 km/hour i.
C. 2.67 km/hour i.
D. 2.67 km/hour.
E. 7.00 km/hour.

Expert Solution

Part 11

The ship starts at x= +400 km, y= -200km and undergoes three displacements D_1, D₂and D₃.

Initial coordinates in vector form = $(400 \hat{i} - 200 \hat{j})$ km

$\vec{D_{3}}$ in vector form can be written as: $\vec{D_{3}}$ = $(- 500 \hat{i} - 100 \hat{j})$

Total Displacement of car = $\vec{D_{1}} + \vec{D_{2}}$ $+ \vec{D_{3}}$

Total displacement = $(- 600 \hat{i} + 300 \hat{j}) + (300 \hat{i} - 200 \hat{j})$ + $(- 500 \hat{i} - 100 \hat{j})$

Total displacement = $(- 600 + 300 - 500) \hat{i} + (300 - 200 - 100) \hat{j}$ = $(- 800 \hat{i} + 0 \hat{j})$ km

Final vector = Initial coordinates + Total Displacement

Final vector = $(400 \hat{i} - 200 \hat{j})$ + $(- 800 \hat{i} + 0 \hat{j})$ = $(- 400 \hat{i} - 200 \hat{j})$ km

Final coordinates : x= -400 km , y=-200km

Answer is option A

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