Finding the initial velocity using calculus I throw a stone at 20 degree, when the stone falls to the ground, it reaches 100m further.
Using CALCULUS methods, find the initial velocity of the stone.

The calculus part in this is taking the derivative of $\vec{r}(t)$,which is $\dot{\vec{r}}(t)=\vec{v}(t)$ (the dot above r means derivative with respect to $t$). Most of the used concepts in this example are from physics, though.
Somewhere in your calculation, you must have $x(t)$ and $y(t)$, which represent the position of the stone dependent on time. Assume that the initial time when you throw the stone is $t=0$. Because $\vec{r}(t)=(x(t),y(t))$, $\vec{v}(t)=\dot{\vec{r}}(t)=(\dot x(t),\dot y(t))$, and thus $\vec{v}(0)=(\dot x(0),\dot y(0))$.
The last formula is the "calculus" part of the calculation.
