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## Homework Statement

a student want to cross a river flowing east at a rate of 2.0km/hr in a boat on the south bank and arrive at point L on the north (north and west) side. Point L is 0.5km to the left or west from the starting point (point K - point K is on the south side). Point L is 0.5km (to the left) from a perpindicular line drawn from the starting point (K)

The student can row at 5.0km/hr.

How long will it take to paddle north-west up stream and arrive at point L?

## Homework Equations

the picture

L ----------0.5km ------------M

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....................................0.25km -> flow = 2km / hr

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(K)

## The Attempt at a Solution

It has been a very long time since I have worked these types of problems and just for fun I tried my hand at this - no luck

I said the student can row at 5km/hr north and (5-2) km/hr westward

He will need to paddle the length of the hypotenuse or SQRT((0.25)^2 + (0.5)^2) = 0.559 km

The students velocity vector is SQRT((5)^2 + (3)^2) = 5.83 km/hr.

I see this is wrong - his velocity is faster than he can paddle.

My direction was to acquire his velocity vector and divide the hypotenuse distance (0.5590km) by the new velocity vector.

I know this is wrong - I have the answer - 0.17858 hr.

Am I wrong to think in terms of a velocity vector?

Is this to be solved with simple position equations?

Help??

Thanks

Sparky_