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Math Help - 2D Vector problems

  1. #1
    Newbie sir nerdalot's Avatar
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    2D Vector problems

    Hi,

    i've got a bit stuck with this 2D vector problem!!
    A Car is traveling at 60km/h on a bearing of 078 degrees T. Within the closed car a bee flies at 3m/s diagonally from the rear to the front corner so that its angle of flight is at 37 degrees with the axis of the car. Find the velocity that the bee is flying relative to the ground. Answer to 1 decimal place and bearing to nearest minute.
    Thank you
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    If I understand your question, here is the solution.

    The velocity of the car is 60 kph, at (90 -78) = 12 degrees above the East-axis.
    The velocity of the bee in the car is 3m/sec, at (12 +37) = 49deg above the East-axis.

    Km/h and m/sec.
    Let use km/h all.

    3m/sec *(1km /1000m)(3600sec /1hr) = 3*3600/1000 = 10.8 kph

    So, Easting-components of the two velocities,
    E = 60cos(12deg) +10.8cos(49deg) = 65.774 kph

    Northing-components of the two velocities,
    N = 60sin(12deg) +10.8sin(49deg) = 20.626 kph

    Resultant of E and N,
    R = sqrt[E^2 +N^2]
    R = sqrt[(65.774)^2 +(20.626)^2] = 68.932 kph ---------***

    Bearing, based from North,
    tan(theta) = E/N = 65.774 /20.626 = 3.18888
    theta = arctan(3.18888) = 72.589 degrees = 72deg and 35.34min --------***

    Therefore, relative to the ground, the bee flies at the rate of 68.9 km/h on a bearing of 72deg,35min. ----------------answer.
    Last edited by ticbol; September 4th 2007 at 11:24 AM.
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