5. The force with which the airflow acts on the sail can be calculated using the formula

$F=\frac{B S \rho\left(v_{0}-v\right)^{2}}{2}$, where $B-$ is the aerodynamic force coefficient, $S-$ is the area of the sail $S$ $=7 \mathrm{M}^{2} ; \rho$ - air density, $v_{0}$ - wind speed $v_{0}=6.3 \mathrm{~m} / \mathrm{c}, v-$ is the speed of the sailboat. At some point in time, the instantaneous power of the wind reaches its maximum value. What is the speed of the sailboat at this moment?

Given:

$F=\frac{B S \rho\left(v_{0}-v\right)^{2}}{2}$

$N\left(t^{\prime}\right)=N_{\max }$

$v_{0}=6.3 \frac{M}{c}$

$v\left(t^{\prime}\right)-?$
$$
\begin{aligned}
& \left.\begin{array}{l}
F=f(v) \\
N=F \cdot v
\end{array}\right\} \Rightarrow N=f(v) \\
& N=\frac{B S \rho}{2}\left(v_{0}^{2}-2 v_{0} v+v^{2}\right) v=\frac{B S \rho}{2}\left(v_{0}^{2} v-2 v_{0} v^{2}+v^{3}\right) \\
& N=N_{\max } \Rightarrow N^{\prime}(v)=0 \\
& N^{\prime}(v)=\frac{B S \rho}{2}\left(v_{0}^{2}-4 v_{0} v+3 v^{2}\right)=0 \\
& v_{0}^{2}-4 v_{0} v+3 v^{2}=0 \\
& 3 v^{2}-4 v_{0} v+v_{0}^{2}=0 \\
& v_{1,2}=\frac{4 v_{0} \pm \sqrt{16 v_{0}^{2}-12 v_{0}^{2}}}{6}=\frac{4 v_{0} \pm \sqrt{4 v_{0}^{2}}}{6}=\frac{4 v_{0} \pm 2 v_{0}}{6} \\
& v_{1}=v_{0} \text { (not satisfied) } v_{2}=\frac{v_{0}=3.1 \text { m/s }}{3}
\end{aligned}
$$

## VARIANT 4