5)The position of two towns A and B are (50°N,45°W) and (50°N,K°W) respectively.It takes a plane 5 hours to travel from A to B at an average speed of 800knots.The same plane takes 1 and 1/2 hours to travel from B to another town C at the same average speed.Given that C is to the north of B,calculate to the nearest degree;
a)The value of K
b)The latitude of C
c)If the plane started from A at 9:00am and flew to C through B,find the local time at C when the plane arrived there
a) To find the value of K, we can use the formula Distance = Speed × Time.
From A to B:
Distance = Speed × Time
Distance = 800 knots × 5 hours
Distance = 4000 nautical miles
From B to C:
Time = 1.5 hours
Speed = 800 knots
Distance = Speed × Time
4000 nautical miles = 800 knots × 1.5 hours
4000 nautical miles = 1200 nautical miles
The change in latitude from B to C is 50°N to K°N, so it is 50° - K° = 1200 nautical miles
K = 50° - 1200 nautical miles
K = 1200 nautical miles / 60 nautical miles per degree
K = 20°
Therefore, the value of K is 20°.
b) The latitude of C is 50°N - 20° = 30°N
c) Since the plane started from A at 9:00 am and took 5 hours to travel to B, it arrived at B at 2:00 pm. Then, from B to C it took 1.5 hours.
Therefore, the plane arrived at C at 2:00 pm + 1.5 hours = 3:30 pm local time.