1)If I head across a river paddling my canoe at 6km/h N, but the river current is moving at 3km/h E, determine the speed and direction of my canoe relative to the shore.
Given:
$\displaystyle v_{cr} = 6 km/h\ N$
$\displaystyle v_{re} = 3 km/h\ E$
$\displaystyle v_{ce} =\ ?$
cr: canoe with respect to river
re: river with respect to earth
ce: canoe with respect to earth
First, for speed remember that in order to get $\displaystyle v_{ce}$, I need to have a velocity who subscript starts with c and ends with e. Thus:
$\displaystyle v_{ce} = v_{cr} + v_{re}$
Use Pythagorus theorem to find v_{ce} now:
$\displaystyle v_{ce}^2 = v_{cr}^2 + v_{re}^2$
Second, for direction, use tangent ratio:
$\displaystyle \tan{\theta} = \frac{v_{cr}}{v_{re}}$
Be careful though! When you get the angle, make sure you state the direction correctly. If you found the angle using this ratio:
$\displaystyle \tan{\theta} = \frac{v_{cr}}{v_{re}}$
Then direction is: The direction of $\displaystyle v_{cr}$ of The direction of $\displaystyle v_{re}$.
This question is related to the Pythagoras theorem. You can solve this problem by using Pythagoras theorem. It will be easy to solve when you apply it in the question.
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jerry
Wide Circles