An air traffic controller observes two airplanes approachingthe airport. The displacement from the control tower to plane 1is given by the vector A>, which has a magnitude of 220 km andpoints in a direction 32° north of west. The displacement from thecontrol tower to plane 2 is given by the vector B>, which has a magnitude of 140 km and points 65° east of north. (a) Sketch the vectors A>, -B>, and D>= A>- B>. Notice that D>is the displacementfrom plane 2 to plane 1. (b) Find the magnitude and direction ofthe vector D>

Vector A is in the direction 39 0° clockwise from the -y-axis. The T-component of A is A, = -12.0 m.

A unit vector m is along the positive x-axis and the unit vector n in quarant II. The angle betweenthem is 104°. Draw a vector diagram of 3n-2m and then find the magnitude of |3n+2m|, correctto the nearest tenth.

A jogger travels a route that has two parts. The first is a displacement A of 2.30 km due south, and the second involves a displacement B that points due east. The resultant displacement A + B has a magnitude of 4.75 km. (a) What is the magnitude of B, and (b) what is the direction of A + B as a positive angle relative to due south? Suppose that A - B had a magnitude of 4.75 km. (c) What then would be the magnitude of B, and (d) what is the direction of A - B relative to due south? (a) Number (b) Number (c) Number (d) Number Mi i Mi Units Units Units Units <

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The magnitude of Ais 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis. What is the x-component?

A pilot needs to fy to a destination 350 km north of his current position in 2.0 hours. An air traffic controller tells him that the wind velocity (as seen on the ground) is 27 km/h [E34 °S]. a) Sketch the overall vectors of the plane to the ground, the plane to the air and the air to the ground. Write the equation for the velocity of the plane relative to the ground with the appropriate subscripts. b) What is the minimum speed that the pilot would need to fly if there was no wind? c) Determine the heading of the plane (in what direction must the pilot fly to compensate for the wind?). Show your work. Label your vectors and label x and y components. d) Determine the speed of the plane with respect to air that the pilot would need to take in order to reach the desired destination on time.

You start on the origin and walk in a strait line to a point that is 10 m east and 25 m north of where you started. From there you walk 3 m west and another 10 m north, Write each location in terms of vectors A and B. Use vector addition as well.