# Math

An aeroplane flies from town A(20°N,60°E) to townB (20°N,20°E)
if the journey takes 6 hours
Calculate correct to 3 significant figures, the average speed of the aeroplane
If it then flies due north from town B to town C 420km away.calculate to the nearest degree the latitude of town C

1. 👍
2. 👎
3. 👁
1. Approximate the earth as a perfect sphere, with radius 6371 km.

Change in longitude = 60-20 = 40° = 40π/180 radians
Latitude of flight path = 20° N
horizontal radius = Rcos(20°)

Horizontal arc length from A to B
=Rcos(20°)(40π/180)
=6371*0.9397*.6981
=1506.6 km

1506.6 km took 6 hours, so
average ground speed
=1506.6/6
=251.1 km/hr

travelling due north another 420 km subtends an angle
=420/6371 radians
=0.06593 radians
=0.06593*180/π °
=3.78°

Latitude of town C
=20+3.78
=23.78°N

1. 👍
2. 👎
2. No formula

1. 👍
2. 👎
3. No formula

No formula

1. 👍
2. 👎

## Similar Questions

1. ### Maths

An aeroplane flies from a town x on a bearing of N45°E o another town y,a distance of 200km.it then changes course and flies to another town zon a bearing of s60°e.if z is directly east of x,calculate to correct 3significant

2. ### Mathematics

An aeroplane leaves an airport A and flies on a bearing 035°for 1.5 hours at 600km/hr to airport B It then flies on a bearing 130° for 1.5hours at 400km per hour to an airport C calculate the distance from C to A and the bearing

3. ### Maths

An Aeroplane X Whose Average Speed Is 500km/h Leaves Kano Airport At 7:00am And Travels For 2 Hours On A Bearing 050 Degree. It Then Changes Course And Flies On A Bearing 120 Degree To An Airstrip A. Another Aeroplane Y Leaves

4. ### math

An aeroplane flies due north from Ikeja Airport for 500km. It then flies on a bearing of 060 degrees for a further distance of 300km before overflying a road junction.Calculate a. The distance of the aeroplne from Ikeja Airport

1. ### Maths

An aeroplane flies from a town X on a bearing of N 45 degree E to another a town Y on a distance of 200km.it then changes course and flies to another town Z on a bearing of S 60 degree E.if Z is directly east of X.Calculate (a)

2. ### algebra

It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant rate, and that Todd’s

3. ### maths

an aeroplane takes 40 minutes less to fly 3600km with the wind blowing at 30 km/hr than the time it takes to fly against the same wind .Find the actual speed of the aeroplane when there is no wind.

4. ### Maths

An aeroplane flies due north from Ikeja airport for 500km.if their flies on a bearing of 060 for a further distance of 300km before overflying a road junction . calculate the distance of the aeroplane from Ikeja airport when it

1. ### math

A cyclist travels for 60km at x km/h and 180km at y km/h and takes 10 hours altogether for the journey. If the speed are interchange, the journey takes 8.6 (8 whole number 2 over 3) hours. Find x and y.

2. ### math

An aeroplane flies from a town p on(lat.40N,38E)to another town Q on (Lat.40N,22W).It later flies to a third town T on(Lat.28N,22W). Calculate the average speed at which the aeroplane will fly from P to T via Q, If the journey

3. ### algebra

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the

4. ### mathematics

An aeroplane leaves an international airport and flies due north for 1hour at 500km/hr. It then flies for 30 minutes at 800 kilometres/ hour on a bearing of North 53 degrees East. Calculate it's distance and bearing from the