Solve each problem. See Examples 1 and 2. Distance between Two...

Question

Solve each problem. See Examples 1 and 2. Distance between Two Ships A ship leaves its home port and sails on a bearing of S 61°50'. Another ship leaves the same port at the same time and sails on a bearing of N 28°10'E. If the first ship sails at 24.0 mph and the second sails at 28.0 mph, find the distance between the two ships after 4 hr.

Accepted Answer

Bam leaves his office on a bike at a bearing of north 54 degrees 20 minutes east at a speed of 50 kilometers per hour. At the same time, his boss leaves in the car at the bearing of south, 35 degrees, 40 minutes east at a speed of 80 kilometers per hour, determine the distance between them after five hours where we have four possible answers all in kilometers. Now, to solve this, let's first draw a diagram. We have our office right here in the middle. We know Sam leaves at a bearing of north 54 degrees 20 minutes east. So we won't go to the north and in the direction of east, we will draw a vector. Let's say it's roughly right here. Now, we also need to find the bosses bearing which is south, 35 degrees for the east. So we will go to the south and in the direction of the east, we will draw our vector which roughly is right there. Now, we can make a vector between our two points after five hours. Now, let's go ahead and find our missing side link of the Strangle. Let's see if we have a right angle first to do this. Let's find our missing angles in here. For this angle, we will subtract 54 degrees, 20 minutes from 90 to get degrees, 40 minutes. We do the same or other angle in the south. We would get 54 degrees, 20 minutes. Those would add together to equal 90 which means we do have a right triangle there. Since we have a right triangle, we can find our missing side length using the Pythagorean formula. And we'll call these point A and B from the origin to A. We can see that Sam was traveling at a speed of 50 kilometers per hour for five hours. We can then multiply it 55 that distance Sam traveled would be 250 kilometers or the bus he was traveling at a speed of 80 kilometers per hour for five hours. This means his distance was 400 kilometers. Now, since this is a red triangle, we can use Pythagorean theorem. Distance A B will then be the square root of distance A squared plus distance B squared from the origin, we get A B equals the square root of squared plus 400 squared. No speaking the square root of 222,500. If we were to simplify this by taking the square root, we get A B is approximately 471.70 kilometers. This means the answer to our problem is then answer D ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Bearing and Direction in Navigation

Vector Representation of Displacement

Law of Cosines for Distance Calculation

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