After leaving an airport, a plane flies for 1.75h at a speed of 200km/h on a course of 100 degrees. The plane then flies for 2 hours at a speed of 250km/h on a course of 40 degrees. At this time, how far from the airport is the planee?
I wonder if you're in my math class....
I could be wrong with this... but at least here's a possible answer. (It doesn't make much sense)
x^2=500^2+350^2-2x500x350xcos(60 degrees)=
444.4 km
As far as the simple, guaranteed right part goes, remember to multiple 1.75 times 200, and 2 times 250 for the lengths, as that is the time the planes spent flying, so it is the lengths of the sides of your triangle.
If the answer I gave is actually right, I swear I am a genius.
But I only have a 95% in the class. Then again, that's the second-highest grade. :P
Well, let me calculate that for you... but first, let me ask you, is the plane afraid of getting lost and asking for directions? Because I haven't seen many planes with GPS systems yet.
To find the distance from the airport, we can break down the plane's motion into two components: the northward component and the eastward component.
For the first leg, the plane flies for 1.75 hours at a speed of 200 km/h on a course of 100 degrees. Let's calculate the components of its motion:
Northward Component: 200 km/h * cos(100 degrees)
Eastward Component: 200 km/h * sin(100 degrees)
Using a calculator, we get:
Northward Component: 200 km/h * cos(100 degrees) ≈ -77.27 km/h
Eastward Component: 200 km/h * sin(100 degrees) ≈ 187.32 km/h
During the first leg, the plane travels a distance of:
Distance = Speed * Time
Distance = 200 km/h * 1.75 h ≈ 350 km
For the second leg, the plane flies for 2 hours at a speed of 250 km/h on a course of 40 degrees. Let's calculate the components of its motion:
Northward Component: 250 km/h * cos(40 degrees)
Eastward Component: 250 km/h * sin(40 degrees)
Using a calculator, we get:
Northward Component: 250 km/h * cos(40 degrees) ≈ 191.26 km/h
Eastward Component: 250 km/h * sin(40 degrees) ≈ 160.79 km/h
During the second leg, the plane travels a distance of:
Distance = Speed * Time
Distance = 250 km/h * 2 h = 500 km
To find the total distance from the airport, we need to add the distances from both legs:
Total Distance = Distance of Leg 1 + Distance of Leg 2
Total Distance = 350 km + 500 km ≈ 850 km
Therefore, at this time, the plane is approximately 850 km away from the airport.
To find the distance from the airport, we need to calculate the displacement of the plane after each leg of the journey and then find the resultant displacement.
First, let's calculate the displacement for the first leg of the journey. We can use the formula:
displacement = speed * time
Given that the speed of the plane is 200 km/h and the time is 1.75 hours, we can calculate the displacement of the first leg as:
displacement1 = 200 km/h * 1.75 h = 350 km
Next, let's calculate the displacement for the second leg of the journey. Again, using the formula:
displacement = speed * time
Given that the speed of the plane is 250 km/h and the time is 2 hours, we can calculate the displacement of the second leg as:
displacement2 = 250 km/h * 2 h = 500 km
Now, we have the displacements for both legs of the journey:
displacement1 = 350 km
displacement2 = 500 km
To find the resultant displacement, we need to add these two displacements together. However, since the displacements involve both magnitude and direction, we need to treat them as vectors.
Using vector addition, we can calculate the resultant displacement:
Resultant displacement = displacement1 + displacement2
To do this, we need to break down the displacements into their north-south and east-west components using trigonometry.
For displacement1:
north-south component = displacement1 * cos(100 degrees)
east-west component = displacement1 * sin(100 degrees)
For displacement2:
north-south component = displacement2 * cos(40 degrees)
east-west component = displacement2 * sin(40 degrees)
Now, let's calculate the components:
north-south component1 = 350 km * cos(100 degrees)
east-west component1 = 350 km * sin(100 degrees)
north-south component2 = 500 km * cos(40 degrees)
east-west component2 = 500 km * sin(40 degrees)
Now, add the north-south and east-west components individually:
north-south component = north-south component1 + north-south component2
east-west component = east-west component1 + east-west component2
Finally, we can use the Pythagorean theorem to find the magnitude of the resultant displacement:
resultant displacement = sqrt(north-south component^2 + east-west component^2)
By substituting the values into the equation, we can calculate the distance from the airport.