Question

A penny moving at speed v slides off the horizontal surface of a coffee table a vertical distance y from the floor.
(a) Show that the penny lands a distance

Answer 1

Equations of motion of a penny are as follows

$$x(t)=v_0t\\ y(t)=H-\frac{gt^2}{2}$$

When penny lands $y=0$, hence

$$t^*=\sqrt{\frac{2H}{g}}$$

$$L=x(t^*)=v_0\sqrt{\frac{2H}{g}}$$