March 25, 2017

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Three points P, Q and R are on a level ground. Q is 240m from P on a bearing of 230°. R is 120m to the east of P.

(a) Using a scale of 1cm to represent 40m, draw a diagram to show the positions of P, Q and R in the space provided below.
(b) Determine :

(i) the distance of R from Q;
(ii) the bearing of R from Q

(c) A vertical post stands at P and another one at Q. A bird tales 18 seconds to fly directly from the top of the post at Q to the top of the post at P. Given that the angle of depression of the top of the post at P from the top of the post at Q is 9°

(i) The distance, to the nearest meter, the bird covers;
(ii) The speed of the bird in km/h

  • math - ,

    if P is at (0,0), then we have
    Q: (-184,-154)
    R: (120,0)

    so, RQ = 341
    bearing = 180° + arctan(304/154) = 243°

  • math - ,

    d = 341/cos9° = 345m
    speed = 345m/18s * 1km/1000m * 3600s/hr = 69km/hr

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