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This question is incomplete, the missing diagram is uploaded along this answer below;
Answer:
the speed Vc of the current and its direction measured clockwise from the north is 0.71 m/s and 231.02° respectively
Explanation:
Given the data in the question and as illustrated in the diagram below;
The absolute velocity of the ship Vs is 6 Knots due east
so we convert to meter per seconds
Vs = 6 Knots × = 3.0866 m/s
Next we determine the relative velocity of the ship Vs/c
Vs/c = AB / t
given that distance between A to B = 10 nautical miles which requires 2 hours
so we substitute
Vs/c = 10 nautical miles / 2 hrs
Vs/c = [10 nautical miles × ] / [ 2 hrs ×
]
Vs/c = 18520 / 7200
Vs/c = 2.572 m/s
Now, from the second diagram below, { showing the relative velocity polygon }
Now, using COSINE RULE, we calculate the velocity current.
Vc = √( V²s + V²s/c - 2VsSs/ccos10 )
we substitute
Vc = √( (3.0866)² + (2.572)² - (2 × 3.0866 × 2.572 × cos10 ) )
Vc = √( (3.0866)² + (2.572)² - (2 × 3.0866 × 2.572 × 0.9848 ) )
Vc = √( 9.527099 + 6.615184 - 15.6361 )
Vc = √0.506183
Vc = 0.71 m/s
Next, we use the SINE RULE to calculate the direction;
Vc/sin10 = Vs/c / sinθ
we substitute
0.71 / sin10 = 2.572 / sinθ
0.71 / 0.173648 = 2.572 / sinθ
4.0887 = 2.572 / sinθ
sinθ = 2.572 / 4.0887
sinθ = 0.62905
θ = sin⁻¹( 0.62905 )
θ = 38.98°
So, angle measured clock-wise will be;
θ = 270° - 38.98°
θ = 231.02°
Therefore, the speed Vc of the current and its direction measured clockwise from the north is 0.71 m/s and 231.02° respectively
