An aeroplane leaves a point on latitude 54degree south at 10 a.m. It flies due south at a steady speed of 800km/h.
(a) what is its latitude at mid-point?
(b) at what time does it pass over the south pole?
circumference of earth is roughly 40000km
latitude 54 south is 36 degrees from pole.
36/360 * 40000 = 4000 km
4000/800 = 5 hours to the pole.
(a) Well, if the airplane is flying due south, it will maintain its latitude of 54 degrees south at the midpoint.
(b) As for when the airplane passes over the south pole, it's hard for me to say. Maybe it gets invited to a penguin party and decides to hang out there for a while. Or perhaps it takes a wrong turn and ends up at the North Pole. Who knows? Airplanes can be quite adventurous!
To answer these questions, we need to calculate the distance traveled by the airplane and the time it takes to reach the mid-point and the South Pole.
(a) To find the latitude at the mid-point, we need to determine how far the airplane travels from its starting point. Since the airplane flies due south, the latitude decreases at a constant rate.
The South Pole is located at latitude 90 degrees south, and the starting point is at latitude 54 degrees south. Therefore, the airplane needs to cover a distance of 90 - 54 = 36 degrees of latitude.
To convert this into distance, we can use the fact that each degree of latitude is approximately 111 km. So, the distance traveled is 36 degrees * 111 km/degree = 3,996 km.
Since the airplane is flying at a steady speed of 800 km/h, the time taken to cover this distance is given by the formula: time = distance / speed. Hence, time = 3,996 km / 800 km/h = 4.995 hours.
Since the airplane leaves at 10 a.m., the mid-point is reached after approximately 4.995 hours. Adding this to the starting time, we find that the airplane reaches the mid-point at 10 a.m. + 4.995 hours = 2:59 p.m.
Therefore, the latitude at the mid-point is 54 degrees south.
(b) To determine the time at which the airplane passes over the South Pole, we need to calculate the time it takes to cover the entire distance from the starting point to the South Pole.
Using the same formula: time = distance / speed, we find that the time taken is 3,996 km / 800 km/h = 4.995 hours.
Since the airplane leaves at 10 a.m., the time it passes over the South Pole is 10 a.m. + 4.995 hours = 2:59 p.m.
Therefore, the airplane passes over the South Pole at 2:59 p.m.
To solve this problem, we can use some basic concepts about the Earth's latitude and apply them to the given information. Let's break it down step by step:
(a) What is its latitude at the midpoint?
1. We know that the plane flies due south, which means it maintains a longitude line throughout its journey.
2. Since it starts at a latitude of 54 degrees South, we can assume that its latitude decreases by 800 km every hour due to its constant speed.
3. The midpoint of the journey will be when the plane has traveled half of the distance from its starting point to the South Pole.
To calculate the latitude at the midpoint, we can use the following equation:
Latitude at Midpoint = Initial latitude - (Change in latitude per hour * Time to the midpoint)
Since the plane travels with a constant speed, the time to reach the midpoint is half of the total time taken to reach the South Pole.
Given that the plane starts at 10 a.m. and its steady speed is 800 km/h, we can calculate the time to the midpoint:
Time to midpoint = (Time to pass the South Pole) / 2
(b) At what time does it pass over the South Pole?
To calculate the time it takes to pass over the South Pole, we first need to know the distance from the starting point to the South Pole. Since the plane flies due south, the distance is equal to the initial latitude of 54 degrees.
Using the distance and the constant speed of 800 km/h, we can calculate the time it takes to reach the South Pole:
Time to pass the South Pole = Distance / Speed
Once we have the time, we can add it to the initial departure time of 10 a.m. to determine at what time the plane passes over the South Pole.
Remember to convert the latitude to a negative value when subtracting the change in latitude.
I hope this explanation helps you solve the problem step by step!