An aero plane leaves a point on latitude 54 degree south at 10am in the morning. It flies due south at a steady speed of 800km/hr .(A)calculate it's latitude at midday. (B) at what time does it pass over the south-pole
To calculate the latitude at midday, we need to determine the distance traveled by the airplane during that time.
Step 1: Calculate the time elapsed between 10 am and midday.
Midday is 12 pm, which means 2 hours have passed.
Step 2: Calculate the distance traveled in 2 hours.
The airplane flies at a steady speed of 800 km/hr. In 2 hours, it would have covered a distance of 800 km/hr * 2 hr = 1600 km.
Step 3: Calculate the final latitude.
The airplane is initially at latitude 54 degrees south. Since it is flying due south, the latitude decreases as it travels. The latitude change is equivalent to the distance traveled along a meridian.
1 degree of latitude along a meridian is approximately equal to 111 km. Therefore, the latitude change can be calculated as follows:
Latitude change = Distance traveled / (1 degree of latitude / km)
= 1600 km / (111 km/degree)
= 14.41 degrees
Now we can determine the final latitude:
Latitude at midday = Initial latitude - Latitude change
= 54 degrees south - 14.41 degrees
= 39.59 degrees south
Therefore, the latitude at midday is approximately 39.59 degrees south.
To calculate the time at which the airplane passes over the South Pole, we need to determine the distance from the starting point to the South Pole and divide it by the airplane's speed.
Step 1: Calculate the distance from the starting point to the South Pole.
The distance from any point to the South Pole along a meridian is one-fourth of Earth's circumference, which is approximately 10,000 km.
Step 2: Calculate the time needed to cover the distance.
Time = Distance / Speed
= 10,000 km / 800 km/hr
= 12.5 hours
Therefore, the airplane will pass over the South Pole 12.5 hours after it starts.
To determine the exact time, we add the time it started at 10 am:
Time at the South Pole = Start time + Time needed to cover the distance
= 10 am + 12.5 hours
= 10 am + 12 hours + 30 minutes
= 10:30 pm
Therefore, the airplane will pass over the South Pole at 10:30 pm.
To solve this problem, we can use the formula:
Distance = Speed × Time
(A) To calculate the latitude at midday, we need to find the distance traveled by the airplane in 2 hours (from 10 am to 12 pm).
Step 1: Calculate the distance traveled:
Distance = Speed × Time
Distance = 800 km/h × 2 h
Distance = 1600 km
Step 2: Convert the distance to degrees of latitude:
1 degree of latitude = 111 km (approximately)
Latitude = Distance ÷ 111 km
Latitude = 1600 km ÷ 111 km
Latitude ≈ 14.41 degrees
Therefore, at midday, the airplane's latitude is approximately 14.41 degrees south.
(B) To calculate the time when the airplane passes over the South Pole, we need to find the total distance from the departure point to the South Pole and then divide it by the speed of the airplane.
Step 1: Find the total distance to the South Pole:
The South Pole is located at 90 degrees south latitude.
Total distance = 90 degrees × 111 km/degree (approximately)
Total distance ≈ 9990 km
Step 2: Calculate the time to reach the South Pole:
Time = Distance ÷ Speed
Time = 9990 km ÷ 800 km/h
Time ≈ 12.49 hours
Since the airplane departs at 10 am, it will pass over the South Pole approximately 12.49 hours later.
Step 3: Calculate the time of arrival:
Time of arrival = Departure time + Time taken
Time of arrival = 10 am + 12.49 hours
Therefore, the airplane will pass over the South Pole at approximately 10:29 pm.