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The duck is floating in the middle of the round pond. It wants to join others, unfortunately there is a fox on the bank. The duck cannot take of from water. It can take of only from the ground. Calculate the minimum ratio of the speeds of the duck and the fox for duck to be able to reach the bank and take off and not be eaten by fox. Suggest suitable strategy to reach this goal.

Small ball is hanging at the end of mass-less string and oscillates around equilibrium (see figure) at frequency $f$. What will be its frequency $f'$ if the length of the string is half of original length?

* The position of point mass in time in Cartesian coordinates is described by position vector $\vect{r}(t) =(R \cos\(\omega t\)$,R sin\(\omega t\),d)\,.$$ Calculate, what is time dependence of vectors $v(t)$ and $a(t)$. Calculate tangential, normal and bi-normal component of acceleration.

• A wheel of radius $R$ rolls without slipping at straight track at velocity $v$. A point is connected with the wheel at the distance $r$ from the centre of wheel. Calculate its movement and the velocity as function of the time in coordinate system connected with the Earth. Can the speed be zero at some moment?