11. If a navigation error puts a plane 2.5° off course, how far off course is the plane after flying for 2 hours at 152 miles per hour?
off course as measured how?
Actual distance between target and position, or
distance perpendicular to the intended course?
In the first case, use the law of cosines. Both sides of the included angle are 152*2
To find out how far off course the plane is after flying for 2 hours at 152 miles per hour due to a 2.5° navigation error, you can follow these steps:
Step 1: Convert the 2.5° navigation error to a distance.
- Since the navigation error is given in degrees, we need to convert it to a distance. We'll assume a flat Earth approximation for simplicity.
- One degree of longitude at the equator is approximately equal to 69 miles. So, one mile is equal to approximately 1/69th of a degree of longitude.
- Therefore, the distance corresponding to a 2.5° navigation error is 2.5 * 69 miles.
Step 2: Calculate the total distance flown by the plane.
- The plane flies for 2 hours at a speed of 152 miles per hour. Therefore, the total distance flown is 2 hours * 152 miles per hour.
Step 3: Calculate the off-course distance.
- Subtract the distance flown from the distance corresponding to the navigation error to get the off-course distance. This will give us the magnitude of the off-course distance.
Now, let's plug in the values and calculate:
Step 1: 2.5° * 69 miles ≈ 172.5 miles (distance corresponding to the navigation error)
Step 2: 2 hours * 152 miles per hour = 304 miles (total distance flown)
Step 3: 172.5 miles - 304 miles ≈ -131.5 miles (off-course distance)
Therefore, the plane is approximately 131.5 miles off course after flying for 2 hours at 152 miles per hour due to a 2.5° navigation error. The negative sign indicates that the plane is off course to the left of its intended path.