## Oblique Throw (Height, Time, Velocity)

` $$ y(t) ~=~ y_0 ~+~ v_{\text y0} \, t ~-~ \frac{1}{2}\,g\,t^2 $$ `

Here you will learn the laws of **motion of bodies** (e.g. particles, cars, planets) under the influence of **mechanical forces**. Master the power to predict the future location and state of these bodies - whether the body is particle-like or wave-like.

` $$ y(t) ~=~ y_0 ~+~ v_{\text y0} \, t ~-~ \frac{1}{2}\,g\,t^2 $$ `

` $$ \class{blue}{v} ~=~ \sqrt{ {\class{blue}{v_0}}^2 ~+~ 2a\,(x - x_0) } $$ `

Derivation of the velocity formula for the elastic head-on collision of two different masses using conservation of momentum and conservation of energy.

` $$ \begin{align}
v'_1 ~&=~ v_2 \, \left(\frac{2m_2}{m_1 ~+~ m_2}\right) \\\\
v'_2 ~&=~ v_2 \, \left(\frac{m_2 ~-~ m_1}{m_1 ~+~ m_2}\right)
\end{align} $$ `

` $$ m_1 \, \class{red}{v_1} ~+~ m_2 \, \class{blue}{v_2} ~=~ m_1 \, \class{red}{v'_1} ~+~ m_2 \, \class{blue}{v'_2} $$ `

` $$ \varphi ~=~ \omega_0 \, t ~+~ \frac{1}{2} \, \class{red}{\alpha} \, t^2 $$ `

` $$ \class{blue}{ v_{\text p} } ~=~ \frac{ \class{red}{ \lambda } }{ T } $$ `

` $$ v_{\text p} ~=~ \lambda \, f $$ `