$\"\"$

\

The acceleration of sail boat is proportional to the difference between velocities of the wind and the boat is $\"\"$ .

\

$\"\"$ , where $\"\"$ is a proportional constant, $\"\"$ is the velocity of wind and $\"\"$ is the velocity of boat.

\

Consider $\"\"$ .

\

$\"\"$

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Exponentiate each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(a)

\

When $\"\"$ , the velocity of wind is $\"\"$ and the boat is at rest $\"\"$ .

\

When $\"\"$ , the boat velocity is $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Apply natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

(b)

\

The distance traveled by boat is $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) $\"\"$ .