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9 votes
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​

User Daviid
by
6.2k points

1 Answer

1 vote

Answer:

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

Explanation:

The distance covered by each boat after 2.5 hours are:

speed =
(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 =
√(3250)

= 57.0088

x = 57.0 m

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

User Daniel Tull
by
6.8k points
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