Question

The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 43.0 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 4.20 h after it passes over the island?

Answer 1

Based on the bearings and speed and time provided, the distance of the hurricane 4.2 hours after it passed over the Grand Bahama Island is 157.9 km.

How far from Grand Bahama is the hurricane 4.20 h after it passes over the island?

The distance between the hurricane and Grand Bahama island is determined from calculations by using their bearings from each other.

Let:

• the Grand Bahama island be represented with A.
• the point 60° N of west be B.
• the final point due north be C.
• the distance AB be c
• the distance BC be a
• thedistance AC be b

The three points form a triangle ABC with the angle at B being 150°

Total time = 4.2 hours

Time spent in travelling at a speed of 43 km/h = 3 hours

Time spent in travelling at a speed of 27 km/h = 4.2 - 3 = 1.2 hours

The distance a = 1.2 × 27 = 32.4 km

The distancec = 43 × 3 = 129 km

Using the cosine rule:

${b}^{2} = {a}^{2} + {c}^{2} - 2ac \cos(b)$

${b}^{2} = {32.4}^{2} + {129}^{2} - 2 \times 32.4 \times 129 \cos(150)$

$b = 157.9 \: km$

Therefore, the distance of the hurricane 4.2 hours after it passed over the Grand Bahama Island is 157.9 km.

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