1. The eye of a hurricane passes over Grand Bahama Island in a direction 30.0° north of west with a speed of 42.0 km/h. The hurricane goes this direction for three hours. Then the course of the hurricane suddenly shifts due north. From this point, its speed is 27.0 km/h for two more hours. Convert the velocity vectors to position vectors. Write the position vectors as a magnitude and angle. (remember to measure the angles from the positive x axis) 30°N/w O - 180° 30 150° 42 Kmh * 3h= 136km * 3h= 126とm %3D Y2 a7km/h x 2h:54km doplacoment NoRth b. Assuming Grand Bahama Island is at (0,0), draw a sketch of the two position vectors representing the path of the hurricane. Remember that North is the positive y axis and that east is the positive x axis. Vz - 54 Km 30 W--- O, 0 Determine the components of each of the two position vectors. Vly: (63 km (y-Comi) 176km xSin30° : (03km C. (x-Comp) Yzx= Okm ( Yix=-109.12 Kkm -/26とmxcos30°=109.12km Yay = 54Km d. Add the two vectors to determine the resultant position vector. e. What is the distance from Grand Bahama Island to the final position of the hurricane?
1. The eye of a hurricane passes over Grand Bahama Island in a direction 30.0° north of west with a speed of 42.0 km/h. The hurricane goes this direction for three hours. Then the course of the hurricane suddenly shifts due north. From this point, its speed is 27.0 km/h for two more hours. Convert the velocity vectors to position vectors. Write the position vectors as a magnitude and angle. (remember to measure the angles from the positive x axis) 30°N/w O - 180° 30 150° 42 Kmh * 3h= 136km * 3h= 126とm %3D Y2 a7km/h x 2h:54km doplacoment NoRth b. Assuming Grand Bahama Island is at (0,0), draw a sketch of the two position vectors representing the path of the hurricane. Remember that North is the positive y axis and that east is the positive x axis. Vz - 54 Km 30 W--- O, 0 Determine the components of each of the two position vectors. Vly: (63 km (y-Comi) 176km xSin30° : (03km C. (x-Comp) Yzx= Okm ( Yix=-109.12 Kkm -/26とmxcos30°=109.12km Yay = 54Km d. Add the two vectors to determine the resultant position vector. e. What is the distance from Grand Bahama Island to the final position of the hurricane?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Pt. d&e

Transcribed Image Text:1. The eye of a hurricane passes over Grand Bahama Island in a direction 30.0° north of
west with a speed of 42.0 km/h. The hurricane goes this direction for three hours. Then the
course of the hurricane suddenly shifts due north. From this point, its speed is 27.0 km/h
for two more hours.
Convert the velocity vectors to position vectors. Write the position vectors as a
magnitude and angle. (remember to measure the angles from the positive x axis)
a.
30N/w
* V:1260km
44: ん
42 Km h * 3h = 126km
O - 180°
30
150 0
の
raa a7kmlh x 2h: 54km
doplaement NORth
b. Assuming Grand Bahama Island is at (0,0), draw a sketch of the two position vectors
representing the path of the hurricane. Remember that North is the positive y axis
and that east is the positive x axis.
Vz -54 Km
30
0, 0
Determine the components of each of the two position vectors.
Vly: (63 km (y-cami)
176km xsin30 (03km
C.
(x-Comp)
Vax= Okm (NO x-comp)
ix=-109.12 Km
-/26とmxco5.30°= 109.12Km7
Yay = 54km
d. Add the two vectors to determine the resultant position vector.
e.
What is the distance from Grand Bahama Island to the final position of the
hurricane?
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