Answer to Question #172476 in Classical Mechanics for Jethro Torio

Question

Show that the velocity of impact at the ground of an object thrown vertically upward is equal to the initial velocity of the upward throw.

Answer 1

Let $v$ is the velocity of the upward throw, $u$ is the velocity of impact at the ground.

$0=v-gt,$ $\implies$ $t=\frac vg,$

$s=vt-\frac{gt^2}{2}=\frac{v^2}{g}-\frac{v^2}{2g}=\frac{v^2}{2g};$

$s=\frac{gt'^2}{2}\implies t'=\sqrt{\frac{2s}{g}}=\sqrt{\frac{v^2}{g^2}}=\frac vg=t,$

$u=gt'=g\cdot \frac vg=v\implies u=v.$