Answer:
The distance between the ships is 87.84 km.
Explanation:
Given that,
Angle of first ship= 40°
Speed of first ship = 18 knots
Angle of second ship= 130°
Speed of second ship = 26 knots
We need to calculate the resultant velocity
Using cosine rule
[tex]v=\sqrt{v_{1}^2+v_{2}^2-2v_{1}v_{2}\cos\theta}[/tex]
Put the value into the formula
[tex]v=\sqrt{18^2+26^2-2\times18\times26\times\cos90}[/tex]
[tex]v=\sqrt{18^2+26^2}[/tex]
[tex]v=\sqrt{324+676}[/tex]
[tex]v=10\sqrt{10}[/tex]
We need to calculate the distance between the ships
[tex]d =v\times t[/tex]
Put the value into the formula
[tex]d=10\sqrt{10}\times1.5\times1.852[/tex]
[tex]d=87.84\ km[/tex]
Hence, The distance between the ships is 87.84 km.
