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​

Answer 1

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.