Answer to Question #259280 in Classical Mechanics for Tithi

Question

Say, Mr. X runs on a plain land and jumps from a spot in forward direction. Recognize and describe his jumping motion through an equation and make an argument for your answer.

Answer 1

$\text{Let at the moment of the jump mr.X has the following speeds:}$

$v_x - \text{instantaneous speed of movement horizontally }$

$v_y - \text{instantaneous vertical speed}$

$\text{Then the coordinates mr.X will be:}$

$x = v_xt(1)$

$y = v_yt -\frac{gt^2}{2}(2)$

$\text{The equations (1) and (2) coincide with the parametric}$

$\text{ equations of a body thrown at an angle to the horizon.}$

$\text{Where:}$

$v=\sqrt{v_x^2+v_y^2} \text{ -body speed}$

$\tan \alpha= \frac{v_y}{v_x};\alpha-\text{throw angle}$