ilorin is at 8.5 degree to the north,4.6 degree to the east and free town at 8.5degree to the north,13.3degree to the west calculate(a)their distance apart,measured along the parallel of latitude(b)their distance from the equqtor(c)their speed in km/h due to the rotation of the earth
The answer to d question
answer to d question
answer to the question
A student
I live in Lagos
B.distance from the equator
Formula is ;lant X69
=Lant 8.5X69=586.5mile or metre
C. Speed in Km/ sec
=2πRCoslantitude/24 hrs
2X 3.142 X6400 XCos 8.5
=39.78Km /sec
To calculate the distance between Ilorin and Freetown, measured along the parallel of latitude, you can use the formula for calculating the distance between two points on a sphere using longitude and latitude. Here are the steps to follow:
(a) Distance apart measured along the parallel of latitude:
1. Convert the given degrees to radians. To convert degrees to radians, multiply by π/180.
- For Ilorin: Latitude = 8.5° * (π/180) = 0.1484 radians
- For Freetown: Latitude = 8.5° * (π/180) = 0.1484 radians
2. Calculate the absolute difference between the longitudes of the two locations:
- Longitudes: Ilorin = 4.6° E, Freetown = 13.3° W
- 4.6° + 13.3° = 17.9° difference
3. Convert the longitude difference to radians:
- Longitude difference = 17.9° * (π/180) = 0.312 radians
4. Calculate the great circle distance using the formula:
- Distance = Radius of Earth * ArcCos(Sin(Lat1)*Sin(Lat2) + Cos(Lat1)*Cos(Lat2)*Cos(Long2-Long1))
- Assuming the radius of the Earth is approximately 6,371 kilometers:
- Distance = 6,371 km * ArcCos(Sin(0.1484)*Sin(0.1484) + Cos(0.1484)*Cos(0.1484)*Cos(0.312))
Using a scientific calculator to calculate the above expression will give you the distance in kilometers.
(b) Distance from the equator:
To calculate the distance from the equator, use the latitude of each location:
For Ilorin: Distance from Equator = 8.5° * 111.32 km
For Freetown: Distance from Equator = 8.5° * 111.32 km
(c) Speed in km/h due to the rotation of the Earth:
The speed due to the rotation of the Earth depends on the latitude. It is highest at the equator and gradually decreases towards the poles. The speed at any latitude can be calculated using the formula:
Speed = Circumference of Earth * (Cos(latitude) * (2π)/(24 hours))
Assuming the radius of the Earth is approximately 6,371 kilometers and a day has 24 hours, substitute the latitude of each location into the formula to obtain their respective speeds.
Please note that the values obtained from these calculations are approximate due to the assumption of the Earth's radius and the simplification of the Earth as a perfect sphere.
For ilorin,we will use I
While for Freetown,we will use F
e.i I(lat8.5°N,long 46°E)
F(lat 8.5°N,long 13.3°W )
A.difference in longitude/360X2πRcoslantitude
46+13.3/360 X2X3.142XCos 8.5°N
1.024Km