physics

An airplane flies 200 km due west from city A to city B and then 270 km in the direction of 31.0° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?

  1. 👍
  2. 👎
  3. 👁
  1. AC = 200 km @ 180o + 270 km @ 149o.

    X=Hor.=200*cos180 + 270*cos149=-431.4 km
    Y=Ver.=200*sin180 + 270*sin149=139.1 km.

    a. (AC)^2 = X^2 + Y^2 = 205,454.77
    AC = 453.3 km.

    b. tanA = Y/X = 139.1/431.4 = 0.32244
    A = 17.9o North of West.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to

  2. physics

    An airplane flies 200 km due west from city A to city B and then 260 km in the direction of 32.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? ?km (b) Relative to city A, in

  3. math

    The distance between city A and city B is 500 miles. On a certain wall map, this is represented by a length of 2.3 feet. On the map, how many feet would there be between city C and city D, two cities that are actually 800 miles

  4. History

    How did the geographic location of Philadelphia affect the city's development? Because of its location on rivers, the city built bridges and used ferries to allow workers to access the city. Because of proximity to water, streets

  1. Physics

    An airplane flies 400 km west from city A to city B, then 200km northwest to city c and finally 100 km north to city D. How far it is from city a to d?

  2. math

    An airplane is flying from Montreal to Vancouver. The wind is blowing from the west at 60km/hour. The airplane flies at an airspeed of 750km/h and must stay on a heading of 65 degrees west of north. A) what heading should the

  3. Math

    An airplane needs to head due north, but there is a wind blowing from the southwest at 85 km/hr. The plane flies with an airspeed of 550 km/hr. To end up flying due north, how many degrees west of north will the pilot need to fly

  4. trig

    City A is 300km due east of city B. City C is 200km on a bearing of 123¤ from city B. How far is it from C to A?

  1. physics

    A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north to

  2. Mathematics

    City y is 200km and in the direction of 048 from city x. City x is 80km and in the direction of 108 from city y. Find the distance of city z from city x and the bearing of city x from z

  3. physics

    Three cities X,Y, and Z are connected by straight highways. City X is 6 km from city Y, city Y is 4 km from city Z, and city X is 5 km from city Z. Find the angle made by the highways XY and YZ?

  4. Calculus

    The pilot of an airplane that flies with an airspeed of 800 km/h wishes to travel to a city 800 km due east. There is a 80 km/h wind FROM the northeast a) what should the plane's heading be? b) How long will the trip take?

You can view more similar questions or ask a new question.