An airplane flying at 550 miles per hour has a bearing of 53°. After flying for 2.5 hours, how far north and how far east will the plane have traveled from its point of departure?
I'm having a REALLY hard time with this one. I don't know what I'm doing wrong. Can someone walk me through this?
Why don't airplanes ever tell jokes? Because the altitude would go over your head! But don't worry, I'm here to help you with your problem.
To solve this question, we'll need to break it down into smaller steps. First, let's find out how far the plane will travel in those 2.5 hours. We can do this by multiplying the speed (550 miles/hour) by the time (2.5 hours):
550 miles/hour * 2.5 hours = 1,375 miles
So the plane will travel 1,375 miles in 2.5 hours.
Now, let's find out how far north and how far east the plane will travel. To do this, we'll use the bearing of 53°. The bearing tells us the direction in which the plane is traveling, relative to north.
To find out how far the plane will travel north, we'll use trigonometry. We'll use the sine function, which relates the length of the side opposite an angle to the length of the hypotenuse. In this case, the length of the side opposite the angle of 53° represents the distance north.
sin(53°) = opposite/hypotenuse
The hypotenuse is the distance the plane traveled (1,375 miles), and the opposite side is the distance north. Rearranging the formula, we get:
opposite = sin(53°) * 1,375 miles
Calculating that, we find:
opposite ≈ 1,080.5 miles
So the plane will travel approximately 1,080.5 miles north.
To find out how far the plane will travel east, we'll use the cosine function, which relates the length of the side adjacent to an angle to the length of the hypotenuse. In this case, the length of the side adjacent to the angle of 53° represents the distance east.
cos(53°) = adjacent/hypotenuse
Again, the hypotenuse is the distance the plane traveled (1,375 miles), and the adjacent side is the distance east. Rearranging the formula, we get:
adjacent = cos(53°) * 1,375 miles
Calculating that, we find:
adjacent ≈ 938.6 miles
So the plane will travel approximately 938.6 miles east.
In summary, after flying for 2.5 hours at a speed of 550 miles per hour with a bearing of 53°, the plane will have traveled approximately 1,080.5 miles north and 938.6 miles east from its point of departure.
To solve this problem, we can break it down into two components: the northward distance (y-axis) and the eastward distance (x-axis) that the airplane has traveled.
Step 1: Determine the northward distance
Since the plane is flying at a bearing of 53°, we can use trigonometry to find the northward distance. The angle between the plane's velocity vector and the north direction is 90° - 53° = 37°.
To find the northward distance, we can use the sine function: sin(angle) = opposite/hypotenuse.
Let's call the northward distance "y".
sin(37°) = y/550
550 * sin(37°) = y
y ≈ 325.51 miles (rounded to two decimal places)
Therefore, the plane has traveled approximately 325.51 miles northward.
Step 2: Determine the eastward distance
Similarly, we can use trigonometry to find the eastward distance. The angle between the plane's velocity vector and the east direction is 53°.
To find the eastward distance, we can use the cosine function: cos(angle) = adjacent/hypotenuse.
Let's call the eastward distance "x".
cos(53°) = x/550
550 * cos(53°) = x
x ≈ 364.28 miles (rounded to two decimal places)
Therefore, the plane has traveled approximately 364.28 miles eastward.
In summary, after flying for 2.5 hours at a speed of 550 miles per hour with a bearing of 53°, the plane will have traveled approximately 325.51 miles northward and 364.28 miles eastward from its point of departure.
Sure! I can help you with that. To solve this problem, we can break it down into two parts: calculating the distance traveled and determining the eastward and northward components of the displacement.
First, let's calculate the distance traveled by the plane. The formula for distance is speed multiplied by time. In this case, the speed of the plane is given as 550 miles per hour and the time is given as 2.5 hours. So, the distance traveled would be:
Distance = Speed × Time
Distance = 550 miles/hour × 2.5 hours
Distance = 1375 miles
Therefore, the plane will have traveled 1375 miles from its point of departure.
Now, let's determine the eastward and northward components of the displacement. To do this, we'll use trigonometry and the bearing of the plane.
Given that the bearing of the plane is 53°, we can use this angle to find the northward and eastward components. Since we know the total distance traveled is 1375 miles, we can use trigonometric functions to find the lengths of each component.
The northward component can be found using the sine function (sin) since it is the side opposite the angle:
Northward component = Distance × sin(bearing)
Northward component = 1375 miles × sin(53°)
Northward component ≈ 1059.89 miles (rounded to the nearest hundredth)
The eastward component can be found using the cosine function (cos) since it is the side adjacent to the angle:
Eastward component = Distance × cos(bearing)
Eastward component = 1375 miles × cos(53°)
Eastward component ≈ 920.03 miles (rounded to the nearest hundredth)
Therefore, the plane will have traveled approximately 1059.89 miles north and approximately 920.03 miles east from its point of departure.
If you are using standard notation, then a bearing of 53° would be 53° clockwise from North
make a sketch.
Start the plane at the origin, then draw a line 53° form the y-axis (NOrth) and make it 2.5(550) or 1375 miles long. Complete the right-angled triangle, whose base angle will be 37°
distance north:
y/1375 = sin37
y = 827.5 miles
distance east:
x/1375 = cos 37
x = 1098.1 miles