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Kinematics

Problem 1.28

A small body is thrown at an angle to the horizontal with the initial velocity \(\mathbf{v}_{0}\). Neglecting the air drag, find: (a) the displacement of the body as a function of time \(\mathbf{r}(t)\) (b) the mean velocity vector \(\langle\mathrm{v}\rangle\) averaged over the first \(t\) seconds and over the total time of motion.

Reveal Answer
(a)r=v0t+gt2/2;(b)⟨v⟩t==v0+gt/2,⟨v⟩=v0−g(v0 g)/g2\begin{aligned} & (\mathrm{a}) \mathbf{r}=\mathbf{v}_{0} t+\mathrm{g} t^{2} / 2 ;(\mathrm{b})\langle\mathbf{v}\rangle_{t}=\\ =& \mathbf{v}_{0}+\mathrm{g} t / 2, \quad\langle\mathbf{v}\rangle=\mathbf{v}_{0}-\mathrm{g}\left(\mathbf{v}_{0} \mathrm{~g}\right) / g^{2} \end{aligned}
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