An aeroplane leaves a point on latitude 54°S at 10 a.m.it flies due south at a steady speed at 800km/h. (a)what is the latitude at mid-day(b) At what time does it pass over the south pole

Why would you post half of the solution

1 degree of latitude is about 111 km. So,

800 km/hr ≈ 800/111 = 7.2°/hr

so, ...

U no get sense o

Why u go post 1/2 of the answer na

(a) Well, since the airplane is flying due south, it will maintain the same latitude throughout its journey. So, at mid-day, the latitude of the airplane will still be 54°S. Hopefully, it packed a good sunscreen!

(b) Ah, the south pole is a slippery one to catch! The airplane cannot pass directly over the south pole while flying due south. To reach the south pole, the plane would have to change its direction and travel due north. So, it won't pass over the south pole at any time during its journey. It's better off leaving the pole dancing to the penguins!

To determine the latitude at mid-day, we need to calculate how much the plane has traveled southward from its starting point at 54°S.

Given that the plane flies at a steady speed of 800 km/h, we can calculate the distance traveled in 2 hours (from 10 a.m. to mid-day). Since the plane flies due south, the distance traveled is equal to the speed multiplied by the time:

Distance = Speed × Time
Distance = 800 km/h × 2 h
Distance = 1600 km

Therefore, the plane has traveled 1600 km southward from its starting point. Now, we need to calculate the latitude of this new location.

To do this, we can use the concept of meridians and parallels. Meridians are the lines that run from the North Pole to the South Pole, while parallels are the lines that run parallel to the equator.

Each degree of latitude is approximately 111 km. Since the plane has traveled 1600 km southward, we divide this distance by 111 km/degree to find the change in latitude:

Change in Latitude = Distance Traveled / (111 km/degree)
Change in Latitude = 1600 km / (111 km/degree)
Change in Latitude ≈ 14.41 degrees

Given that the plane started at 54°S, we subtract the change in latitude from the starting latitude to find the latitude at mid-day:

Latitude at Mid-Day = Starting Latitude - Change in Latitude
Latitude at Mid-Day = 54°S - 14.41°
Latitude at Mid-Day ≈ 39.59°S

Therefore, the latitude at mid-day is approximately 39.59°S.

Now, let's determine at what time the plane passes over the South Pole.

Since the plane started flying at 10 a.m. and flies at a steady speed of 800 km/h, we can calculate the time it takes to travel from the starting point to the South Pole.

The distance from the starting point to the South Pole is approximately half the circumference of the Earth, which is 20,003.93 km. Therefore, the time taken to travel from the starting point to the South Pole is given by:

Time = Distance / Speed
Time = 20,003.93 km / 800 km/h
Time ≈ 25 hours

Therefore, the plane will pass over the South Pole approximately 25 hours after it leaves the starting point at 10 a.m. To find the time, we add 25 hours to the starting time:

Time of Passing the South Pole = 10 a.m. + 25 hours
Time of Passing the South Pole = 11 a.m. the next day

Thus, the plane will pass over the South Pole at 11 a.m. the next day.