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:
[tex]{b}^{2} = {a}^{2} + {c}^{2} - 2ac \cos(b) [/tex]
[tex] {b}^{2} = {32.4}^{2} + {129}^{2} - 2 \times 32.4 \times 129 \cos(150) [/tex]
[tex]b = 157.9 \: km[/tex]
Therefore, the distance of the hurricane 4.2 hours after it passed over the Grand Bahama Island is 157.9 km.
Learn more about bearing and distance at: https://brainly.com/question/25424147
