An airplane leaves an airport,flies due north for 2 hours at 500 km/h. It then flies on a bearing of 53 degree at 300 km/h for 90 minutes. Find the bearing of the plane from the airport. If it takes the airplane 150 minutes to fly back to the airport,find the average speed of the airplane for the whole flight
This should get you started
https://www.jiskha.com/questions/1826597/an-aeroplane-leaves-an-airport-flies-due-north-for-2hrs-at-500km-h-it-then-flies-on-a#2023378
To find the bearing of the plane from the airport, we can use trigonometry.
First, let's break down the information given:
- The plane flies due north for 2 hours at a speed of 500 km/h.
- Then, it changes direction and flies on a bearing of 53 degrees for 90 minutes at a speed of 300 km/h.
- It takes the plane 150 minutes to fly back to the airport.
Now, let's find the bearing of the plane from the airport:
1. Convert the time of flight to hours:
- 90 minutes is equivalent to 90/60 = 1.5 hours.
- 150 minutes is equivalent to 150/60 = 2.5 hours.
2. Calculate the total distance traveled by the plane:
- Distance = Speed * Time.
Distance flown north = 500 km/h * 2 hours = 1000 km.
Distance flown at 53 degrees = 300 km/h * 1.5 hours = 450 km.
3. Use the Law of Cosines to find the distance from the airport to the point where the plane changed direction:
- c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle opposite side c.
Let's assume that the distance from the airport to the point of direction change is represented by c.
Applying the Law of Cosines, we have:
c^2 = (1000 km)^2 + (450 km)^2 - 2 * 1000 km * 450 km * cos(53 degrees).
4. Calculate c using the above equation.
Now, to find the bearing of the plane from the airport:
5. Use the Law of Sines to find the angle opposite the distance from the airport to the point where the plane changed direction:
- sin(A)/a = sin(C)/c, where A is the angle opposite side a.
Let's assume that the bearing of the plane from the airport is represented by A.
Applying the Law of Sines, we have:
sin(A)/1000 km = sin(53 degrees)/c.
6. Calculate A using the above equation.
Once you've found the value of A, you'll have the bearing of the plane from the airport.
To find the average speed of the airplane for the whole flight:
7. Calculate the total distance traveled by the plane, including the return journey:
- Total distance = Distance flown north + Distance flown at 53 degrees + Distance flown back to the airport.
Total distance = 1000 km + 450 km + 1000 km = 2450 km.
8. Calculate the total time taken for the entire flight:
- Total time = Time flown north + Time flown at 53 degrees + Time flown back to the airport.
Total time = 2 hours + 1.5 hours + 2.5 hours = 6 hours.
9. Use the formula: Average Speed = Total Distance / Total Time.
Average Speed = 2450 km / 6 hours.
Once you've completed these steps, you will have found the bearing of the plane from the airport and the average speed of the airplane for the whole flight.