Resultant direction of aircraft

The resulting vector will have both direction and magnitude. How is it oriented? What is its length?In summary, the problem involves finding the direction and magnitude of the velocity vector of a control-configured aircraft, given a wind vector and a controlled vector of the aircraft's direction and speed. After calculating the unit vectors for the wind and aircraft, the actual velocity vectors can be found by multiplying the unit vectors by the given speeds. Then, the resulting vectors can be added to find the final velocity vector, which will have both direction and magnitude.
  • #1
gkraju
16
0

Homework Statement



in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ?


Homework Equations





The Attempt at a Solution


i calculated unit vector of direction of wind.
also i calculated unit vector of direction of aircraft
i do not know what to do afterwards ?
 
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  • #2
gkraju said:

Homework Statement



in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ?


Homework Equations





The Attempt at a Solution


i calculated unit vector of direction of wind.
also i calculated unit vector of direction of aircraft
i do not know what to do afterwards ?

What is the velocity vector of the plane? What happens if you add the velocity vectors of the wind and plane?
 
  • #3
A "velocity vector" should point in the right direction and its length should be the speed. After you have found the unit vectors in each direction, multiply by the given speed (45 knots for the winds speed, 2450 knots for the airplane [Which is, by the way, about 4 times the speed of sound- what kind of airplane is this?]) to get the actual velocity vectors. Then, as berkeman says, add them by adding the corresponding components.
 

Related to Resultant direction of aircraft

What is the resultant direction of an aircraft?

The resultant direction of an aircraft is the vector sum of all the forces acting on the aircraft, including the thrust, lift, drag, and weight forces.

How is the resultant direction of an aircraft calculated?

The resultant direction of an aircraft is calculated using vector addition. This involves breaking down each individual force into its horizontal and vertical components, and then adding them together to find the final resultant direction.

Why is the resultant direction of an aircraft important?

The resultant direction of an aircraft is important because it determines the direction in which the aircraft will move. It also affects the stability and control of the aircraft during flight.

What factors can affect the resultant direction of an aircraft?

The resultant direction of an aircraft can be affected by various factors such as the weight and balance of the aircraft, the angle of attack, air density, and wind speed and direction.

How does the pilot control the resultant direction of an aircraft?

The pilot controls the resultant direction of an aircraft by adjusting the control surfaces, such as the rudder, ailerons, and elevators, to change the direction and stability of the aircraft. The pilot also adjusts the thrust and pitch of the aircraft to control the forward motion and altitude.

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