An airplane flying at 600 miles per hour has a bearing of 52 degrees. After flying for 1.5 hours, how far north and how far east will the plane have traveled from point of departure?
(I'm not sure how to convert miles into degrees or if that's even the right thing to do)
To find out how far north and how far east the plane will have traveled, we need to use trigonometry.
First, we need to determine the plane's velocity components in the north and east directions.
The plane's velocity component in the north direction can be calculated using the formula:
Velocity north = Velocity * sin(bearing angle)
Given that the plane is flying at 600 miles per hour and has a bearing of 52 degrees:
Velocity north = 600 * sin(52)
Velocity north = 600 * 0.78801075
Velocity north ≈ 472.8 miles per hour
The plane's velocity component in the east direction can be calculated using the formula:
Velocity east = Velocity * cos(bearing angle)
Velocity east = 600 * cos(52)
Velocity east = 600 * 0.61566148
Velocity east ≈ 369.4 miles per hour
Now, we can calculate the distance traveled in each direction by multiplying the velocity components by the time traveled:
Distance north = Velocity north * Time
Distance north = 472.8 * 1.5
Distance north ≈ 709.2 miles
Distance east = Velocity east * Time
Distance east = 369.4 * 1.5
Distance east ≈ 554.1 miles
Therefore, the plane will have traveled approximately 709.2 miles north and 554.1 miles east from the point of departure.
To calculate the distance traveled in both the north and east directions, we need to use some trigonometry. Let's break down the problem step by step:
1. First, convert the bearing angle from degrees to radians. This is necessary because trigonometric functions in most programming languages work with radians.
To convert from degrees to radians, use the formula:
radians = degrees * (π/180)
So, for a bearing angle of 52 degrees, the calculation would be:
radians = 52 * (π/180)
2. Next, we need to find the northward and eastward components of the plane's velocity. To do this, we'll use trigonometric functions.
The northward velocity component can be calculated as follows:
northward velocity = velocity * cos(bearing angle in radians)
Using the values given, the calculation would be:
northward velocity = 600 * cos(bearing angle in radians)
3. Similarly, the eastward velocity component can be calculated as follows:
eastward velocity = velocity * sin(bearing angle in radians)
Using the values given, the calculation would be:
eastward velocity = 600 * sin(bearing angle in radians)
4. Finally, to find the total distance traveled in the north and east directions, multiply the velocity components by the time traveled.
northward distance = northward velocity * time traveled
eastward distance = eastward velocity * time traveled
Using the values given, the calculations would be:
northward distance = northward velocity * 1.5
eastward distance = eastward velocity * 1.5
By following these steps, you should be able to determine how far north and east the airplane will have traveled from the point of departure.
The bearing of &theta=52 degrees is measured from the north.
At 600 miles per hour for 1.5 hours, the plane would be D=600*1.5=900 miles from the point of departure.
The northing would be D cosθ and the easting would be D sinθ.