R-AESPE-9

Example Question

You can paddle a canoe at 5 km/h in still water and you want to cross a river which is $50m$ wide. The river is flowing at $3km/h$.

If you start from A and paddle directly towards the opposite bank, find the resultant velocity, the time taken to reach the bank and how far you are from B when you arrive.

• Construct a right angled triangle to represent the vector force
• Notice that since the distance to the bank is $50m$, this means there exists a similar triangle between the two opposite points of the bank and the point we land on

  • Hence, the distance between B and the point we land on is proportional to $3km/h$. We know $5km/h => 50m$, hence $d=30m$

Complex but important way to find time:

• Find out the resultant vector.
• Find the distance between A to that point we land on
• Hence, we know distance, we know speed (in the same direction!! important!)

Why can this be cheesed?

• River flows perpendicular to the river.
• Hence, when you construct the diagram, you notice that it has no effect on the vertical vector.
• That is to say, the rate at which we travel vertically is the same regardless of how strong the river pushes horizontally.

What if we must land at point B?

funky math

Exercises to do: 6C

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