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.

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

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

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

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