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Answer:
Direction of the police plane = N57.1E
Speed of the police airplane = 255 km/h
Step-by-step explanation:
The diagram of the situation described is presented in the attached image to this question.
Let the distance the police airplane has to travel to intercept the smuggler at 08:30 be x km
The police airplane moves at 06:30 and plans to intercept the smuggler at 08:30; thereby travelling for 2 hours.
By 08:30, the smuggler would have travelled for 2 hours 30 mins, that is, 2.5 hours, travelling at 200 km/h, that is a total distance of 500 km covered.
So, the paths form a triangle.
Using cosine rule, we can obtain the distance, x, that the police airplane has to travel to intercept the smuggler at 08:30.
x² = 150² + 500² - (2×150×500×cos 85°)
x² = 259,426.63858785
x = 509.34 km
We can obtain the direction, Φ, by finding the angle θ using some rule.
[(Sin 85°)/509.34] = [(Sin θ)/500]
Sin θ = (500 × sin 85°)/509.34 = 0.9779 = 77.94°
From the attached image,
Φ + θ = 90° + 45° = 135°
Φ = 135° - θ = 135° - 77.94° = 57.06° = 57.1°
Therefore,
Speed of police airplane = (distance)/(time) = (509.34/2) = 254.67 km/h = 255 km/h
Direction of the police plane = N57.1E
Hope this Helps!!!
