as it pass over Grand Bahama island, the eye of a.hurricane is moving in a direc

Question

as it pass over Grand Bahama island, the eye of a.hurricane is moving in a direction 61 north of west with.a speed of

8. 2/9 point P rs SerPSE9 3.P.043 My Notes As it passes i er Grand i hama Island, the eye of a hurricane is moving in a direction 61.0° north of west with a speed of 42.2 km/h. (Let i represent east and j represent north.) (a) What is the unit-vector expression for the velocity of the hurricane? Your response differs from the correct answer by more than 10%. Double check your calculations. km/h Your response differs from the correct answer by more than 10%. Double check your calculations. km/h It maintains this velocity for 2.60 h, at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 22.6 km/h. This new velocity is maintained for 1.50 h. (b) What is the unit-vector expression for the new velocity of the hurricane? km/h i 22.6 (c) What is the unit-vector expression for the displacement of the hurricane during the first 2.60 h? km i+ km (d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h? km j (e) How far from Grand Bahama is the eye 4.10 h after it passes over the island? km

Explanation / Answer

Given,

v = 42.2 km/h ; theta = 61 deg

theta = 180 - 61 = 119 deg

a)v = v cos(theta) i + v sin(theta) j

v = 42.2 x cos61 i + 42.2 x sin61 j = -20.46 i + 36.91 j

Hence, v = -20.46 i + 36.91 j

b)The new velocity will be:

v = 22.6 cos90 + 22.6 x sin90 = 0i + 22.6 j

Hence, v = 0i + 22.6 j

c)we know that speec is

v = dist/time => dist = D = time x speed

So for the first 2.6 hrs

D = 2.6 (-20.46 i + 36.91 j )

D = -53.19 i + 95.97 j

d)For the next 1.5 hours

D = 1.5 (0 i + 22.6 j) = 0 i + 33.9 j

Hence, D = 0i + 33.9 j

e) D = sqrt (X^2 + Y^2)

D = sqrt [(-53.19 + 0)^2 + (95.97 + 33.9)^2] = 140.34 km

Hence, D = 140.34 km

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