Applications of Vectors

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Presentation transcript:

Applications of Vectors

Velocity is a vector quantity that refers to "the rate at which an object changes its position." When evaluating the velocity of an object, one must keep track of direction. It would not be enough to say that an object has a velocity of 55 mi/hr. One must include direction information in order to fully describe the velocity of the object. For instance, you must describe an object's velocity as being 55 mi/hr, east.

Speed is a scalar quantity and does not keep track of direction; velocity is a vector quantity and is direction aware. So an airplane moving towards the west with a speed of 300 mi/hr has a velocity of 300 mi/hr, west.

Component Form of a Velocity Vector: Direction angle Speed is the magnitude.

You do this in your calculator to be sure you get it. 1) Find the component form of the velocity vector that represents an airplane descending West at a speed of 100 mph at an angle of 30o below horizontal. The direction angle is 180o + 30o = 210o. Speed is the magnitude. Direction angle 210o 100 mph You do this in your calculator to be sure you get it.

Don’t move on until everyone gets it Your turn……. 2) The speed of the plane is 200 mph and the direction angle is 225 degrees. Find the component form of the vector. Don’t move on until everyone gets it

Using vectors to find speed and direction. A planes course is in a specific direction (airspeed). That is one vector. The wind pushes it in another direction. That is another vector. The resultant vector is the ground speed.

5a) Find the velocity vector for the plane W = 70 mph 45o Direction angle v = airplane vector w = wind vector r = resultant vector magnitude V = 500 mph A bearing of 330o is a direction angle of 120o. 30o 330 0 b) Find the velocity vector for the wind c)Find the velocity vector for the resultant vector r = v + w 5) An airplane is traveling at a speed of 500 miles per hour with a bearing of 330 degrees. The plane reaches a certain point where it encounters a wind with a velocity of 70 miles per hour in the direction N 45o E. What are the resultant speed and direction of the plane?

d)The magnitude of r = resultant speed: e)The direction (bearing) of the resultant vector is found by: QII, N 22.6o W

6) An airplane is flying in the direction of 1480, with an airspeed of 875 kph. Because of the wind, its ground speed is 800 kph and 1400. Find the direction and speed of the wind.

6) We are given the plane vector and the ground speed (resultant) vector. 140o 148o You have to find the wind vector. r 875 v Find the plane vector. Be careful, 148 is the bearing not the direction angle. Find the resultant vector. Be careful, 140 is the bearing not the direction angle.

v (airspeed) + w (wind) = r (groundspeed) therefore w = r - v Find the speed (magnitude) 138.7 kph Reference angle is 68.7o, so the bearing is N21.30E Find the direction of the wind (bearing).

You do #7, 8 and 9.