Answer:
[tex]\displaystyle t=\frac{2v_o}{g}[/tex]
Explanation:
Horizontal Launch
When an object is launched horizontally at a speed vo, it describes a curved called parabola as the speed in the x-direction does not change and the speed in the y-direction increases with time because the gravity makes it return to the ground.
The vertical distance the object (potato) travels downwards is:
[tex]\displaystyle y=\frac{gt^2}{2}[/tex]
The horizontal distance is
[tex]x=v_ot[/tex]
We need to find the time when both distances are equal, thus
[tex]\displaystyle \frac{gt^2}{2}=v_ot[/tex]
Simplifying by t
[tex]\displaystyle \frac{gt}{2}=v_o[/tex]
Solving for t
[tex]\displaystyle \boxed{t=\frac{2v_o}{g}}[/tex]
