Two ships leave from the same port. One ship travels on a bearing of 157 degrees at 20 knots. The second ship travels on a bearing of 247 degrees at 35 knots. (1 knot is a speed of 1 nautical mile per hour).
Calculate the bearing of the second ship from the first, to the nearest minute.
The two courses are 90 degrees apart, so it's just a matter of figuring the angles of the right triangle. If the angle made by the 1st ship is θ, then the bearing of ship 2 from ship 1 is just
(157+180-θ)°
When? after two days? after two hours?
i dont know this was the question i got asked in my textbook and i really need help with this
wrong some how the answer is 276degrees and 45 min
To calculate the bearing of the second ship from the first, we can use the concept of relative bearing. The relative bearing is the angle between the heading of the first ship and the position of the second ship relative to the first.
First, let's convert the speeds from knots to nautical miles per minute (since we want the bearing in minutes). One knot is equal to one nautical mile per hour, so we divide the speed in knots by 60 to get the speed in nautical miles per minute.
For the first ship:
Speed = 20 knots = 20 nautical miles per hour
Speed = 20/60 = 1/3 nautical miles per minute
For the second ship:
Speed = 35 knots = 35 nautical miles per hour
Speed = 35/60 = 7/12 nautical miles per minute
Now, let's calculate the positions of both ships after a certain amount of time. We'll assume they both travel for the same amount of time.
Let's say they travel for t minutes.
For the first ship:
Distance traveled by the first ship = (1/3) * t nautical miles
For the second ship:
Distance traveled by the second ship = (7/12) * t nautical miles
Now, we can calculate the bearing of the second ship from the first.
Using trigonometry, we can calculate the tangent of the angle between the two ship positions. The tangent of this angle is equal to the difference in latitude divided by the difference in longitude.
Tangent(angle) = (Difference in latitude) / (Difference in longitude)
In this case, the difference in latitude is the distance traveled by the second ship (7/12 * t) and the difference in longitude is the distance traveled by the first ship (1/3 * t).
Let's consider the angle between the two ships after t minutes as theta.
Tangent(theta) = (7/12 * t) / (1/3 * t)
Simplifying the expression, we get:
Tangent(theta) = (7/12) / (1/3) = (7/12) * (3/1) = 7/4
Now, we need to find the angle theta in degrees. We can use the inverse tangent (arctan) function to find theta.
Theta = arctan(7/4)
Using a calculator, the angle comes out to be approximately 59.04 degrees.
Therefore, the bearing of the second ship from the first, to the nearest minute, is approximately 59 degrees.