physics

A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, then 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point.

a) Find the magnitude of the third leg of the journey.

b) Find the direction of the third leg of the journey. (Answer = East of North)

Anyone mind helping please.

  1. 👍
  2. 👎
  3. 👁
  1. Break the 3 vectors into components and solve for the unknown vector.
    For this choose
    North is positive y
    East is positive x

    First vector, 2.00km east represented by (2.00km)x + 0(km)y

    Second vector, 3.50km SE represented by (3.50)(cos(315))(km)x + (3.50)(sin(315))(km)y

    Third vector is unknown, represent it by (a)(km)x + (b)(km)y.

    All three vectors added = 5.80(km)x + 0y
    so:
    2.00(km)x + 3.50(cos(315))(km)x + a(km)x = 5.80(km)x
    Solve for a

    0(km)y + 3.50(sin(315))(km)y + b(km)y = 0(km)y
    Solve for b.
    The resulting angle with this method will be relative to the x axis. Adjust the answer to reflect the degrees from the y axis.

    1. 👍
    2. 👎
  2. why is it not 45 degress why 315

    1. 👍
    2. 👎
  3. Here the vector angles are relative to the X axis. So, east would be 0 degrees, north is 90 degrees, west is 180 degree, and south is 270 degrees. So, SE is 270 + 45 = 315. -45 degrees could also be used.

    1. 👍
    2. 👎
  4. 45

    1. 👍
    2. 👎
  5. Dame desu

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science

    Over which part of the globe do the prevailing winds blow west to east? (1 point) between 0°S and 30°S latitude between 60°S and 90°S latitude between 30°N and 60°N latitude between 0ºN and 30°N latitude Which is a

  2. physics

    a 200kg sailboat experiences an eastward force of 3000N by the ocean tide and a wind force against its sails with magnitude of 6000N directed toward the northwest (45 degrees north of west). what is the magnitude of the resultant

  3. Calculus

    Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

  4. physics 152

    The force exerted by the wind on the sails of a sailboat is 500 N north. The water exerts a force of 150 N east. If the boat (including its crew) has a mass of 290 kg, what are the magnitude and direction of its acceleration?

  1. Science

    Which is a difference between global and local winds? A. Local winds occur over a small area, while global winds occur over a large area. B. Local winds blow in from the ocean, while global winds do not. C. Local winds are

  2. Physics

    Matt is attempting to sail a sailboat northeast across the river with a velocity of 13 m/s relative to the current of water. The water current is flowing from south to north at a velocity of 6 m/s. If the angle between the

  3. Physics

    A 15700 kg sailboat experiences an eastward force 22000 N due to the tide pushing its hull while the wind pushes the sails with a force of 80900 N directed toward the northwest (45◦ westward of North or 45◦ northward of West).

  4. physics

    The accelerating force of the wind on a small 200-kg sailboat is 707 N north. If the drag of the keel is 500 N acting west, what is the acceleration of the boat? A) 1.5 m/s2 35 degrees north of east B) 2.5 m/s2 55 degrees north of

  1. math

    A ship sails 50km on a bearing of 080 degrees calculate how far east it travels to the nearest tenth

  2. Physics

    300 kg sailboat accelerates at 0.5 m/s^2 at an angle of 25degrees North of East. Find the magnitude and direction of the force responsible for this accelereation.

  3. Algebra

    You are making a scale drawing of a sailboat using the scale 1 inch: 3 feet. The length of nthe sailboat at its longest point is 36 feet and the height is 54 feet.What should the lenght and height of the sailboat be in your

  4. Geography

    48. Discuss the various patterns of prevailing wind in each area of latitude (low, middle, high) --I posted this yesterday and bobpursley told me I had some wrong information so I fixed up the essay a bit. Is it OK? The air

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