An aircraft in straight and level flight is in a state of horizontal equilibrium. It is flying 120 km/hr in the direction 110* and not correcting for wind. The wind is blowing at 60 km/hr in the direction 340*. Determine the speed and direction the aircraft will actually fly.
if the * is the degrees, then you need to draw the vectors according to their direction. you can use a graph paper and make your own scale: say one unit cube is 10km/hr. then use the protractor to draw the vectors taking an horizontal line as zero degrees. then draw the vectors. you may also need to use pythagoras theorem to get the actual magnitude of each vectors. Then subtract the vectors by inverting the direction of the wind vector (recall vector subtraction). the resultant of the two vectors is the velocity of the plane.
if the * is the degrees, then you need to draw the vectors according to their direction. you can use a graph paper and make your own scale: say one unit cube is 10km/hr. then use the protractor to draw the vectors taking an horizontal line as zero degrees. then draw the vectors. you may also need to use pythagoras theorem to get the actual magnitude of each vectors. Then subtract the vectors by inverting the direction of the wind vector
To determine the speed and direction at which the aircraft will actually fly, you need to consider both the aircraft's velocity and the wind velocity.
The aircraft's velocity vector can be represented by a line with a length of 120 km/hr extending at an angle of 110 degrees from the reference direction (usually North). The wind velocity vector can be represented by a line with a length of 60 km/hr extending at an angle of 340 degrees.
To find the actual speed and direction of the aircraft, we need to add the vectors of the aircraft's velocity and the wind velocity.
1. First, convert the angles from degrees to radians. This can be done by multiplying the degree value by π/180. In this case, 110 degrees is equal to (110 * π) / 180 radians, and 340 degrees is equal to (340 * π) / 180 radians.
2. Next, break down the vectors into horizontal (x) and vertical (y) components. You can use trigonometry to find these components.
The x-component of the aircraft's velocity vector can be calculated using the formula:
x-component = aircraft speed * cos(aircraft angle in radians)
The y-component of the aircraft's velocity vector can be calculated using the formula:
y-component = aircraft speed * sin(aircraft angle in radians)
Similarly, find the x and y components of the wind velocity vector.
3. Add the x-components of the aircraft's velocity and the wind velocity together. Similarly, add the y-components of the two vectors.
The resulting x-component and y-component represent the sum of the two vectors.
4. Use the Pythagorean theorem to find the magnitude (speed) of the resulting vector. The magnitude can be calculated using the formula:
magnitude = sqrt(x-component^2 + y-component^2)
5. Finally, find the direction (angle) of the resulting vector by taking the inverse tangent of the y-component divided by the x-component. This can be expressed as:
angle = atan2(y-component, x-component)
By following these steps, you can determine the speed and direction at which the aircraft will actually fly.