an airplane flying at 550 miles per hour has a bearing of N 52(DEGREES)E. After flying 1.5 hours, how far north and how far east has the plane traveled from its point of departure?
an airplane flying at 550 miles per hour has a bearing of N 58(DEGREES)E. After flying 1.5 hours, how far north and how far east has the plane traveled from its point of departure?
Well, isn't that plane "bearing" quite the burden? Let's see how far it has traveled.
First, we need to break down the velocity into its north and east components.
To find the north component, we use the sine of the angle: sin(52°) = North component/550 mph.
Plugging in the numbers, we get: North component = 550 mph * sin(52°).
To find the east component, we use the cosine of the angle: cos(52°) = East component/550 mph.
Plugging in the numbers, we get: East component = 550 mph * cos(52°).
Since the plane has flown for 1.5 hours, we can multiply each component by that time:
North distance = North component * 1.5 hours.
East distance = East component * 1.5 hours.
So, in conclusion, the plane has traveled "this far north" and "this far east."
To find how far north and how far east the plane has traveled from its point of departure, we can use trigonometry.
Step 1: Convert the bearing to degrees north of east.
The bearing N 52° E can be converted to an azimuth angle by subtracting it from 90°.
90° - 52° = 38°
Step 2: Calculate the distance traveled in the east direction.
The eastward distance can be found using the formula: Distance = Speed × Time
Distance = 550 miles per hour × 1.5 hours = 825 miles
Step 3: Calculate the displacement in the east and north directions.
The displacement is the distance traveled in each direction, given by:
East displacement = Distance × cos(angle)
North displacement = Distance × sin(angle)
Using the calculated distance, the angle in degrees, and the trigonometric functions, we can calculate the east and north displacements.
East displacement = 825 miles × cos(38°)
East displacement ≈ 651 miles (rounded to the nearest mile)
North displacement = 825 miles × sin(38°)
North displacement ≈ 509 miles (rounded to the nearest mile)
Therefore, the plane has traveled approximately 651 miles east and 509 miles north from its point of departure.
To determine how far north and east the airplane has traveled, we can use basic trigonometry. The bearing of N 52° E tells us that the angle between the direction of the plane and the north direction is 52 degrees.
1. First, we need to find the eastward and northward components of the plane's velocity.
To find the eastward component, we can use the formula:
Eastward component = velocity * cos(angle)
Eastward component = 550 mph * cos(52°)
To find the northward component, we can use the formula:
Northward component = velocity * sin(angle)
Northward component = 550 mph * sin(52°)
2. Calculate the eastward and northward displacements by multiplying the components by the time traveled.
Eastward displacement = eastward component * time
Northward displacement = northward component * time
Eastward displacement = (550 mph * cos(52°)) * 1.5 hours
Northward displacement = (550 mph * sin(52°)) * 1.5 hours
Now, let's calculate the values:
Using a calculator, we find:
Cos(52°) ≈ 0.61566147
Sin(52°) ≈ 0.78801075
Eastward component ≈ 550 mph * 0.61566147 ≈ 338.1138085 mph
Northward component ≈ 550 mph * 0.78801075 ≈ 433.9054125 mph
Eastward displacement ≈ 338.1138085 mph * 1.5 hours ≈ 507.1707127 miles
Northward displacement ≈ 433.9054125 mph * 1.5 hours ≈ 650.8581188 miles
Therefore, the plane has traveled approximately 507.17 miles east and 650.86 miles north from its point of departure.
This is what I got.
Plane travelled 825m in 1.5 hrs.
sin(52) = a/825 = 650m N
cos(52) = b/825 = 508m E