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## Homework Statement

A man wishes to cross a river of width 120 m by a motorboat. His rowing speed in still water (or relative to water) is 3 m/s and his

**maximum walking speed is 1 m/s.**The river flows with a velocity of 4 m/s.

(a) Find the path which he should take to reach the point directly opposite to his starting point in the shortest time.

(b) Find the time required to reach the destination.

**
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2. Homework Equations

2. Homework Equations

Let ω be the width of the river and x be the drifting of the boat.

Let

**v**denote the velocity vectors and v denote their respective magnitudes.

v

_{r}= absolute velocity of river

v

_{br}= velocity of boatman relative to the river or velocity of boatman in still water

v

_{b}= absolute velocity of boatman

Hence,

**v**=

_{br}**v**-

_{b}**v**

_{r}∴

**v**=

_{b}**v**+

_{br}**v**

_{r}Time taken to cross the river t = ω/v

_{br-y}= ω/v

_{br}cos θ

Drift x = v

_{b-x}t = (v

_{r}- v

_{br}sin θ)ω/v

_{br}cos θ

## The Attempt at a Solution

Now, in order to reach the point directly opposite to his starting point, resultant velocity

**v**must be perpendicular to the river current.

_{b}So, for this the drift x must be 0.

x = 0 gives v

_{r}= v

_{br}sin θ

Subsituting, sin θ = 4/3, which is meaningless.

I can't proceed without θ. Also, I don't get why they've given his

**maximum walking speed.**

Am I missing anything?

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