An aeroplane flew due west for 3hours from P(50°N,70°W) to point Q at an average speed of 600km\hr, the aeroplane then flew south from Q to point Y 500km away. Calculate the longitude of Q and the latitude of Y
1 degree of latitude is approximately 111 km. So, 500km south takes you to 50-500/111 = 4.5°N
Naturally, the longitude has not changed.
Similarly, for the westward leg,
1 degree of longitude is approximately
111 km*cos(50°)=71.3 km
Since plane was at 70°W, and flew westwards, the longitude would increase.
Use an accurate value of radius of the earth, R, to replace the 111 km.
Formula is
R*π/180.
Find speed then get titer and solve using great circle
To calculate the longitude of point Q, we need to determine how far west the airplane flew from point P. We know that the airplane flew for 3 hours at an average speed of 600 km/hr. Therefore, the westward distance can be calculated as the product of the speed and time:
Westward distance = Speed × Time = 600 km/hr × 3 hours = 1800 km
Since point P is at 70°W longitude, and the airplane flew westward for 1800 km, we can subtract the westward distance from the initial longitude of P to find the longitude of Q:
Longitude of Q = Longitude of P - Westward distance/111
Using this formula, the longitude of Q is:
Longitude of Q = 70°W - 1800 km/111 = 70°W - 16.2° ≈ 53.8°W
To calculate the latitude of point Y, we need to determine how far south the airplane flew from point Q. We are given that the distance from Q to Y is 500 km, but we need to convert this distance into a change in latitude.
We need to know the distance between each degree of latitude. The distance between each degree of latitude is roughly the same regardless of the longitude. Based on the Earth's circumference, we can approximate this distance as 111 km per degree.
Therefore, the change in latitude from Q to Y can be calculated as:
Change in latitude = Distance/111 = 500 km/111
Using this formula, the change in latitude from Q to Y is:
Change in latitude = 500 km/111 ≈ 4.5°
Since point Q is located at latitude 50°N, and the airplane flew 4.5° south, we can subtract the change in latitude from the initial latitude of Q to find the latitude of Y:
Latitude of Y = Latitude of Q - Change in latitude
Using this formula, the latitude of Y is:
Latitude of Y = 50°N - 4.5° ≈ 45.5°N
Therefore, the longitude of Q is approximately 53.8°W, and the latitude of Y is approximately 45.5°N.