Power Boat Races

Hard Applied Maths Question ?

A power boat has cruising speed of 60 km/hr. It is
taking part in a race around three buoys arranged in an equilateral triangle. The
second buoy, B, is 5 km due East of the starting/finishing buoy, A. The third
buoy, C, is to the North of the line joining A and B. There is a current flowing at
10 km/hr from the south-west. In what direction should the boat be steered on
each leg of the race and how long will it take the boat to complete one circuit.

Could someone please give this a go? I don’t have a clue and I need to hand it in tommorow.

Use vectors
A————————>B

……………D
Boat stears in direction AD=60km/h, currentDB10km/h.
<ABD=45
need to find <DAB

Sine rule
sin A / 10 = sin 45 / 60
sinA =10sin45/60
A=6deg 46min

Bearing = (90+6deg 46min)= 096deg46min

<ADB = 128 deg 14 min

to find the speed (thus time)for AB , use cosine rule

AB^2 = 60^2 + 10^2 – 2*60*10cos128 deg 14 min
AB=66.65km/hr

time = 5/66.65=4min30sec

for BC
Boat stears in direction BE=60km/h, current EC=10km/h.

<ECB = 45+30=75
use sine rule for <CBE
Then find bearing

similarly for above

Good luck!

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