3. As it passes over Grand Bahama Island, the eye of a hurricane is moving in a

Question

3. As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 65.0 degrees north of west with a speed of 41.6 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 eye 4.50 h after it passes over the island? Given answer: 162 km 3. As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 65.0 degrees north of west with a speed of 41.6 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 eye 4.50 h after it passes over the island? Given answer: 162 km 3. As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 65.0 degrees north of west with a speed of 41.6 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 eye 4.50 h after it passes over the island? Given answer: 162 km

Explanation / Answer

Let East be +x axis

displacement in the first 3 hours, A = 41.6*3

= 124.8 km

in unit vector notation,

A = -124.8*cos(65) i + 124.8*sin(65) j

= (-52.74 i + 113.1 j) km

in next one and hours the displacement is, B = 27*1.5

= 40.5 km

in unit vector notation, B = 40.5 j km

so, Net displacement, D = A + B

= -52.74 i + 113.1 j + 40.5 j

= (-52.74 i + 153.6 j)km

|D| = sqrt(52.74^2 + 153.6^2)

= 162.4 km <<<<<<<<<<------------------Answer

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