6) Two boats set off from X at the same time (below). Boat A sets off on a bearing of 325° and with a velocity of 14 km/h. Boat B

Question

6) Two boats set off from X at the same
time (below). Boat A sets off on a bearing of 325° and with a velocity of
14 km/h. Boat B sets off on a bearing of 2350 with a velocity of 18 km/h.
Calculate the distance between the boats after they have been travelling
for 2.5 hours. Give your answer to the nearest metre.
A
N
X Х
B​

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Gerda 4 years 2021-09-01T01:10:31+00:00 1 Answers 93 views 0

Answers ( )

  1. Amity
    0
    2021-09-01T01:12:21+00:00
    Reply

    Answer:

    The distance between the two boats after 2.5 hours is 57 m.

    Step-by-step explanation:

    The distance covered by each boat after 2.5 hours are:

    speed = \frac{distance}{time}

    distance = speed x time

    For boat A, speed = 14 km/h and time = 2.5 hrs.

    So that,

    distance = 14 x 2.5

                  = 35 km

    For boat B, speed = 18 km/h and time = 2.5 hrs.

    So that,

    distance = 18 x 2.5

                  = 45 km

    The distance between the two boats after travelling 2.5 hours can be determined by applying the cosine rule. Let the distance be represented by x, so that:

    a^{2} = b^{2} + c^{2} – 2bc Cos A

    x^{2} = 45^{2} + 35^{2} – 2(45 x 35) Cos 90^{o}

       = 2025 + 1225 – 3150 (0)

       = 3250

    x = \sqrt{3250}

      = 57.0088

    x = 57.0 m

    The distance between the two boats after 2.5 hours is 57 m.

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