Home » Maths for Planet Earth » A Speedy Sea Current

A Speedy Sea Current

An ocean current separates into 2 different currents at a small island that can be modelled as the origin. Current A heads due south and current B heads on a bearing of 100˚.

An oceanographer wants to measure the relative surface speeds of these two separate currents, by placing buoys in them off the island and measuring the distance travelled by the buoy in 20 hours.

After 20 hours, the buoy in current A has travelled 150km whilst the buoy in current B has travelled 250km.

a)
Find the average speeds of the two ocean currents.

[2 marks]

b) Calculate the final distance between the buoys.

[2 marks]

c) Θ is the final bearing of the buoy in current B from the buoy in current A. Show that $$\frac{\sin\theta}{\sin{80}} = 0.93$$ to 2 decimal places.

[3 marks]

d) Find the area of the triangle with the island and the two buoys as its
vertices.

[3 marks]

More Maths for Planet Earth

GCSE
Reducing Biodiversity Loss
The graph from the IPBES Global Assessment Report on Biodiversity and Ecosystem Services shows 3 different scenarios for how we could reduce biodiversity loss
A Level
Separated Satellites
2 weather-monitoring satellites orbit the earth. One is in a circular orbit C₁, the other orbits in an extreme ellipse, C₂ so that it can
GCSE
Climate Striking Students
The pie chart shows information about students going to a ‘Fridays for Future’ climate strike. 3360 more female students went to the strike than
A Level
A Carbon Negative Company
A small company’s carbon dioxide (CO₂) emissions since 2000 can be modelled using the parametric equations [12x = t, y = 8t – 4.9t^{2}