The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 degre
ID: 1655875 • Letter: T
Question
The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 degree north of west with a speed of 42.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 27.0 km/h. How far from Grand Bahama is the hurricane 4.10 h after it passes over the island? A map suggests that Atlanta is 730 miles in a direction 5.00 degree north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21.0 degree west of north from Atlanta. The figure below shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to chicago. Magnitude ml direction degree north of east of DallasExplanation / Answer
11. Given,
v1 = 42 km/h
v2 = 27 km/h
t1 = 3 h
t = 4.10 h
theta = 60 deg
Before the shift, the hurricane travels a distance of
d = v1*t1
with a north component of
y1 = d*sin(theta) = v1*t1*sin(theta)
and a west component of
x1 = d*cos(theta) = v1*t1*cos(theta)
After the shift, the hurricane moves a distance
y2 = v2*(t - t1) due north.
The total north displacement is
delta y = y1 + y2
= v1*t1*sin(theta) + v2*(t - t1)
= 42*3*sin(60 deg) + 27*(4.1 - 3)
= 138.82 km
and the total westward displacement is
delta x = d*cos(theta)
= v1*t1*cos(theta)
= 42*3*cos(60 deg)
= 63 km
so the hurricane is now
z = sqrt(delta(x)^2 + delta(y)^2)
= sqrt((63)^2 + (138.82)^2)
= 152.45 km
from the island.
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