A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 665 mi/h, how far is she from her starting position
Question
A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 665 mi/h, how far is she from her starting position
Solution
Step 1: Calculate the distance covered in each leg of the journey.
The pilot flies for 1.5 hours at a speed of 665 mi/h, so the distance covered in the first leg is 1.5 * 665 = 997.5 miles.
Then, she flies for 2 hours at the same speed, so the distance covered in the second leg is 2 * 665 = 1330 miles.
Step 2: Use the law of cosines to find the total distance from the starting point.
The law of cosines states that c² = a² + b² - 2abcos(C), where a and b are the sides of a triangle, C is the angle between them, and c is the length of the third side.
In this case, a = 997.5 miles, b = 1330 miles, and C = 10 degrees. We want to find c, the distance from the starting point.
First, convert the angle to radians: 10 degrees = 10 * π/180 = 0.174532925 radians.
Then, plug the values into the law of cosines:
c² = (997.5)² + (1330)² - 2 * 997.5 * 1330 * cos(0.174532925) c² = 995006.25 + 1768900 - 2 * 997.5 * 1330 * cos(0.174532925) c² = 995006.25 + 1768900 - 2655750 * cos(0.174532925) c² = 995006.25 + 1768900 - 2655750 * 0.984807753 c² = 995006.25 + 1768900 - 2614461.8 c² = 995006.25 + 1768900 - 2614461.8 c² = 156444.45
Finally, take the square root of both sides to find c:
c = sqrt(156444.45) = 395.53 miles.
So, the pilot is approximately 396 miles from her starting position.
Similar Questions
Virginia is flying a Cessna and is descending at a 9°9° angle towards a runway. If she can see a highway behind her at a 45°45° angle that is 300300 meters away from the runway, how much further does she have to fly until she lands? Round to the nearest tenth.
A car is moving ata constant speed of40 km/hr along astraight road which heads towards a large vertical wall andmake a sharp 90° turn by the side of the wall. A fly flying ataconstant speed of 100 km/hr, starts from the wall towards thecaratan instant when the caris20km away, flies until it reachesthe glasspane of the car and returns to the wall at the samespeed. It continues to fly between the car and the wall till thecar makes the 90° turn, (a) What is the total distance the fly hastraveled during this period ? (b) How many trips has it madebetween the car and the wal
Anshul moves towards East a distance of 5 m, then he turns to his left and walks 20 metres, then againhe turns left and walks 15 meters. Now he turns 45° towards his right and goes straight to cover20 2 m meters. How far is he from his starting point ?(1) 40 m (2) 30 m(3) 50 m (4) 55 m
Sania walks 10m in the south direction and then turns left and walks 5m to reach her father’s office; then she walks for 8m after taking a right turn and then she takes a right turn and walks 5m.How far is Sania from her initial position?15m22m20m18m
Joe is walking towards North for 15 miles, turns left and walks another 10 miles. He then turns right and walks 10 miles. Now, he again turns right and walks 30 miles. Which direction is he from Starting point?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.