Tropical storm Nestor evolves as it travels around off the east coast of the Uni

Question

Tropical storm Nestor evolves as it travels around off the east coast of the United States. Nestor starts out at the coordinates x = +300 km, y = 0=-200 km, as shown in the figure. First it undergoes a displacement D_1 = -50 km i + 200 km j, travelling a distance of 300 km in 10 hours. Next it undergoes a displacement D_2 = 100 km i - 300j, travelling a distance of 500 km in 22 hours. Then Nestor stops moving for 8 hours. Finally, it undergoes a displacement D_3 with scalar components D_2x = -50 km, D_3y = 600 km while moving through a distance of 700 km in 10 hours. At the end of the entire journey described above, Nestor is located at coordinates x = 0km, y = -500 km. x = 0km, y = 500 km. x = + 300 km, y = + 300 km. x = -200 km, y = -200 km. x = 500 km, y = 0 km. At the end of the entire journey described above, Nestor has traveled a total distance of 50 km. 500 km in the positive y direction -500 km j. 1500 km in the negative y direction. 1500 km. Nestor's average speed (for the entire journey described above) is 10 km/hour j. 30 km/hour j. 10 km/hour 30 km/hour. 35.7 km/hour. Nestor's overall displacement (for the entire journey describe above) equals +00 km j. -500 km j 1500 km in the negative y direction. -1500 km. 1500 km. For the entire journey described above, the magnitude of the Nestor's average velocity is 11.9 km/hour. 10 km/hour 10 km/hour j. 30 km/hour. -10 km/hour i.

Explanation / Answer

11)

Initial location : Si = 300 i - 200 j

D1 = -50 i + 200j

D2 = 100 i -300 j

D3 = -50 i +600 j

So, final position , Sf = Si + D1 +D2 + D3

So, Sf = 300 i - 200 j + (-50 i + 200j) + (100i - 300j) + (-50 i + 600j)

= ( 300 - 50 +100 ) i + (-200 +200 - 300) j + (-50 i + 600 j)

= 300 i + 300 j <---------- option c

12)

total distance = 300 + 500 + 700 = 1500 km <------ option (e)

NOTE : distance is a scalar quantity.. So, no direction can be specified.

13)

average speed = total distance / total time

= 1500 / (10 +22 +8+10)

= 30 km/hr <----option d

14)

overall displacement = Sf - Si = (300i + 300 j) - (300 i - 200 j)

= 0i + 500 j

= 500 km j <----- option a

15)

average velocity = 500 j / (10 +22 +8+10) = 10 km/hr j

So, magnitude of average velocity = 10 km/hr <------ option b

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