Two ships leave a harbor at the same time. One ship travels on a bearing 15at 18 miles per hourThe other ship travels on a bearing N75E at 10 miles per hourHow far apart will the ships be after 3 hours? The distance is approximately miles. (Round to the nearest tenth as needed.)
To find the distance between the two ships after 3 hours, we can use the formula:
Distance = Rate x Time
First, let's find the distance traveled by the first ship:
Ship 1: 15° at 18 mph
Distance = 18 mph x 3 hours = 54 miles
Now, let's find the distance traveled by the second ship:
Ship 2: N75E at 10 mph can be broken down into two components: North and East
North component = 10 mph x cos(75°)
East component = 10 mph x sin(75°)
North component = 10 mph x cos(75°) = 10 mph x cos(15°) ≈ 9.66 mph
East component = 10 mph x sin(75°) = 10 mph x sin(15°) ≈ 2.59 mph
Distance = sqrt((North component)^2 + (East component)^2) x 3 hours
Distance = sqrt((9.66)^2 + (2.59)^2) x 3 ≈ 10.00 miles x 3 ≈ 30.00 miles
Finally, we can find the total distance between the two ships after 3 hours:
Total distance = sqrt((54)^2 + (30)^2) ≈ 62.4 miles
Therefore, the two ships will be approximately 62.4 miles apart after 3 hours.