I am having trouble with this question.
A privately owned yacht leaves a dock in Myrtke Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S 1.4 degrees E. The yacht averages a speed of 20 knots over the 428-nautical- mile trip.
A. How long will it take the yacht to make the trip?
B. How far east and south is the yacht after 12 hours?
C. A plane leaves Myrtle Beach to fly to Freeport. What bearing should be taken?
I have no idea how to do B and C or where to even begin but for A I got:
20(428/sin1.4), 97 minutes
To solve part A, you correctly used the formula of speed = distance / time. However, there seems to be a unit conversion error in your calculation. The speed of the yacht is given in knots, so the time should be in hours instead of minutes. Let's correct that:
Step 1: Convert the speed from knots to nautical miles per hour (1 knot = 1 nautical mile per hour).
20 knots = 20 nautical miles per hour.
Step 2: Use the formula speed = distance / time to solve for time.
20 nautical miles per hour = 428 nautical miles / time.
time = 428 nautical miles / 20 nautical miles per hour.
Step 3: Calculate the time it will take.
time = 21.4 hours.
So, it will take the yacht approximately 21.4 hours to make the trip.
Now let's move on to parts B and C.
Part B: How far east and south is the yacht after 12 hours?
To solve this, we need to consider the distance traveled in the east-west (east) and north-south (south) directions separately.
Step 1: Calculate the distance traveled in the east direction.
Since the yacht travels at a bearing of S 1.4 degrees E, we can consider the east direction as positive and calculate the distance using the formula east distance = speed × time.
east distance = 20 knots × 12 hours.
Step 2: Calculate the distance traveled in the south direction.
Similarly, since the yacht is heading south (bearing of S 1.4 degrees E), we can consider the south direction as negative and calculate the distance using the formula south distance = speed × time.
south distance = -20 knots × 12 hours.
Step 3: Calculate the distances in nautical miles.
east distance = 20 nautical miles per hour × 12 hours = 240 nautical miles (east).
south distance = -20 nautical miles per hour × 12 hours = -240 nautical miles (south).
Therefore, after 12 hours, the yacht is 240 nautical miles east and 240 nautical miles south from its starting point.
Part C: What bearing should the plane take to fly from Myrtle Beach to Freeport?
To determine the bearing the plane should take, we need to use the concept of directional angles.
Step 1: Convert the bearing of the yacht from degrees to radians.
S 1.4 degrees E can be converted to 1.4 degrees.
Step 2: Convert the directional angle from the yacht's bearing to the bearing for the plane.
Since the plane is flying in the opposite direction of the yacht, the plane's bearing would be the reciprocal of the yacht's bearing.
Plane's bearing = 180 degrees - yacht's bearing.
Step 3: Calculate the plane's bearing.
Plane's bearing = 180 degrees - 1.4 degrees.
Therefore, the plane should take a bearing of approximately 178.6 degrees to fly from Myrtle Beach to Freeport.
To solve part A, you correctly used the formula for calculating time:
Time = Distance / Speed
In this case, the distance is given as 428 nautical miles and the speed is 20 knots. However, you made a small error when converting the time from minutes to hours. Let's correct it:
Time = 428 / 20 = 21.4 hours
To convert this to minutes, multiply by 60:
Time = 21.4 * 60 = 1284 minutes
So, the correct answer for part A is that it will take the yacht approximately 21.4 hours or 1284 minutes to make the trip.
Now let's move on to part B, which asks about the yacht's position after 12 hours.
To find the yacht's position after 12 hours, we need to use its speed and bearing. We'll break down the movement into eastward and southward components using basic trigonometry.
The eastward component can be found using the formula:
Distance East = Distance * sin(Bearing)
Distance East = 428 * sin(1.4)
Using a calculator, we find that the Distance East is approximately 11.85 nautical miles.
The southward component can be found using:
Distance South = Distance * cos(Bearing)
Distance South = 428 * cos(1.4)
Using a calculator, we find that the Distance South is approximately 406.86 nautical miles.
So, after 12 hours, the yacht will have traveled approximately 11.85 nautical miles east and 406.86 nautical miles south.
Finally, let's consider part C, which asks for the bearing the plane should take when flying from Myrtle Beach to Freeport.
To find the bearing, we can use trigonometry and the concept of the tangent of an angle.
The bearing can be found using the formula:
Bearing = atan(Distance East / Distance South)
Bearing = atan(11.85 / 406.86)
Again, using a calculator, we find that the bearing is approximately 1.64 degrees.
Therefore, the plane should take a bearing of approximately N1.64 degrees E when flying from Myrtle Beach to Freeport.
(A) 428nm/20knot = 21.4 hr
the direction does not matter. You have a distance and a speed.
(B)
E: 20*12 sin 1.4°
S: 20*12 cos 1.4°
(C) Surely the same heading (not bearing!) as the yacht, no?
Ignoring water currents and winds aloft.