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Math Help - Relative Motion

  1. #1
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    Relative Motion


    Car A in traveling on a straight road on a bearing of 300 degrees, at a constant speed on 80 km/h. at 10 am it is 15 Km due east of a second car B which is also traveling at a constant speed. assuming that car B can travel in any direction

    a) find the minimum speed of B if it is to intercept A.

    Geomerty doesn't quiet cut this for me

    Thanks Bobak
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobak View Post
    Geomerty doesn't quiet cut this for me

    Thanks Bobak
    Draw a diagram.

    The minimum speed to allow an intercept will involve B moving along a line that meets the course of A at right angles. Then you will have a 30, 60, 90 degree triangle, with one side 15km the one that B moves along 7.5 km and the third along which A mobves of length 7.5*sqrt(3).

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Draw a diagram.

    The minimum speed to allow an intercept will involve B moving along a line that meets the course of A at right angles. Then you will have a 30, 60, 90 degree triangle, with one side 15km the one that B moves along 7.5 km and the third along which A mobves of length 7.5*sqrt(3).

    RonL
    I got V_{min} = \frac{80}{\sqrt{3}} km/h but the books says the velocity is 40 km/h. Who's right me or them ???

    Thanks Bobak
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by bobak View Post
    I got V_{min} = \frac{80}{\sqrt{3}} km/h but the books says the velocity is 40 km/h. Who's right me or them ???

    Thanks Bobak
    Opps, I think what I wrote earlier must be nonsense.

    I'll have to think about the problem some more.

    RonL
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by bobak View Post
    I got V_{min} = \frac{80}{\sqrt{3}} km/h but the books says the velocity is 40 km/h. Who's right me or them ???

    Thanks Bobak
    I am reasonably sure 40 km/hr can't be right.

    RonL
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  6. #6
    Grand Panjandrum
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    OK sorted out the diagram, see attachment, we use the sin rule and conclude the miminum speed for the pursuer occurs when sin(u)=1, and then v=sin(60)*80 km/hr.

    RonL
    Attached Thumbnails Attached Thumbnails Relative Motion-gash.jpg  
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