two airplanes leave an airport at the same time. the velocity of the first airplane is 700 m/h at a heading of 52.2degrees . the velocity of the second is 600 m/h at a heading of 97 degrees . how far apart are they after 3.1 h? answer in units of m.
The angle between them is the difference of the two bearings, each has a leg of velocity*time
Using the law of cosines...
c^2=leg1^2 + leg2^2 -2*leg1*lleg2*cosC
where angle C is the difference of headings.
not sure if i calculated right but is 1562 m the right answer : /
what were your legs,and the angle?
I will check those.
To find the distance between the two airplanes after 3.1 hours, you can use the equations of motion and trigonometry.
First, let's break down the velocities of the two airplanes into their horizontal and vertical components.
For the first airplane:
Velocity = 700 m/h
Heading = 52.2 degrees
The horizontal component of velocity can be found using the cosine function:
Horizontal Velocity (first airplane) = Velocity * cos(Heading)
Horizontal Velocity (first airplane) = 700 * cos(52.2)
The vertical component of velocity can be found using the sine function:
Vertical Velocity (first airplane) = Velocity * sin(Heading)
Vertical Velocity (first airplane) = 700 * sin(52.2)
Similarly, for the second airplane:
Velocity = 600 m/h
Heading = 97 degrees
Horizontal Velocity (second airplane) = Velocity * cos(Heading)
Vertical Velocity (second airplane) = Velocity * sin(Heading)
Now, let's calculate the horizontal and vertical positions of both airplanes after 3.1 hours.
Horizontal Position (first airplane) = Horizontal Velocity (first airplane) * Time
Vertical Position (first airplane) = Vertical Velocity (first airplane) * Time
Horizontal Position (second airplane) = Horizontal Velocity (second airplane) * Time
Vertical Position (second airplane) = Vertical Velocity (second airplane) * Time
Next, we need to calculate the distance between the two airplanes. This can be done using the distance formula:
Distance = sqrt((Horizontal Position [second airplane] - Horizontal Position [first airplane])^2 + (Vertical Position [second airplane] - Vertical Position [first airplane])^2)
Plug in the values you have for the velocities, headings, time, and positions, and calculate the distance. The answer will be in units of meters.