A ship leaves port at 7 am and heads due east at 34 knots. At 10 am, to avoid a storm the ship changes course to N 57° east of north). Find the ships distance from port at 2 pm. Round to the nearest tenth.
To determine nautical miles multiply the speed in knots by the number of hours.
(ex. 10knots in 2hrs would be;
10knots x 2hrs = 20 nautical miles.)
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228.40 naut miles..(straight line distancee from port)
if your asking for total distance from start its: 238 naut mi.
To find the ship's distance from port at 2 pm, we need to break down the problem into two parts: the distance traveled from 7 am to 10 am, and the distance traveled from 10 am to 2 pm.
1. Distance from 7 am to 10 am:
The ship traveled due east at a speed of 34 knots for 3 hours. To find the distance traveled, we can multiply the speed (34 knots) by the number of hours (3 hours):
34 knots x 3 hours = 102 nautical miles.
2. Distance from 10 am to 2 pm:
At 10 am, the ship changed course to N 57° east of north. This means that the ship is now heading in a direction that is 57 degrees east of the north direction. Let's call this direction 'D'.
To find the distance traveled in this direction, we need to use some trigonometry. Let's draw a right triangle where the angle 'D' is the angle between the north direction and the ship's new heading.
In this right triangle, the side opposite to angle 'D' represents the distance traveled in the new direction, and the hypotenuse represents the total distance traveled. We know that the distance traveled opposite to angle 'D' is the same as the distance traveled in the north direction due to the change in course.
Let's call the distance traveled opposite to angle 'D' as 'x'. Since the ship has traveled for 4 hours from 10 am to 2 pm at an unknown speed, we can calculate the distance traveled in the new direction by multiplying '4 hours' by 'x'. However, this distance is equal to the distance traveled in the north direction, which we already calculated in step 1.
So we can equate the distance traveled in the new direction (4 hours * x) to the distance traveled in the north direction (102 nautical miles):
4 hours * x = 102 nautical miles.
Now, we can solve for 'x' by dividing both sides of the equation by 4:
x = 102 nautical miles / 4 hours = 25.5 nautical miles.
So, the ship traveled 25.5 nautical miles in the new direction (N 57° east of north) from 10 am to 2 pm.
To find the total distance from the port at 2 pm, we need to sum up the distances traveled in both directions:
Total distance = distance from 7 am to 10 am + distance from 10 am to 2 pm
Total distance = 102 nautical miles + 25.5 nautical miles = 127.5 nautical miles.
Therefore, the ship's distance from port at 2 pm is approximately 127.5 nautical miles (rounded to the nearest tenth).