1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Relative Velocities & Vectors

  1. Sep 29, 2009 #1
    Relative Velocities & Vectors [MULTIPLYING/DIVIDING VECTORS]

    1. The problem statement, all variables and given/known data

    A bush pilot wants to fly her plane to a lake that is 250.0 km [N30°E] from her starting point. The plane has an air speed of 210. km/h, and a wind blowing from the west at 40.0 km/h.

    (a) In what direction should she head the plane to fly directly to the lake?

    (b) If she uses the heading determined in (a), what will be her velocity relative to the ground?

    2. Relevant equations

    c^2 = a^2 + b^2

    3. The attempt at a solution

    http://img340.imageshack.us/img340/1715/phy1.jpg [Broken]

    (a) sin0 = 40/210
    0 = sin-1(0.19)
    0 = 10.95°
    0 = Degree

    30° - 10° = [N20°E]

    (b) Va^2 = Val^2 + Vwa^2
    = 210^2 + 40^2
    = 44,100 + 1600

    Va = √45, 700
    Va = 213.7m/s

    4. The answers from the textbook

    (a) N20.5°E

    (b) 227 km/h [N30.0°E]

    So how come I am getting different answers? :s
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 29, 2009 #2
    Re: Relative Velocities & Vectors [MULTIPLYING/DIVIDING VECTORS]

    I have no idea what you're trying to do here. Suppose the airspeed makes an angle
    A east of north. What are the north/south and east/west components of the airspeed?
    And what are the components of the ground speed?
    what is the angle the ground speed makes with north, if you know the n/s and e/w components?

    you can only use pythagoras if the Val and Vwa are at right angles.
  4. Sep 29, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    To begin with, your drawing shows the wind blowing from the East, assuming that North is straight up. You need to reverse its direction.

    Secondly, 210 km/h is the speed of the plane relative to the air not the lake.

    You need to treat this as a relative velocity problem in two dimensions where you have to keep the vertical and horizontal components separate from each other. Let

    vPL = velocity of plane relative to the lake (what you are looking for)
    vAL=velocity of plane relative to the lake
    vPA=velocity of plane relative to the air

    Then vPL=vAL+vPA

    Remember that this is vector addition.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook