Question

You use a slingshot to launch a potato horizontally from the edge of a cliff with speed v0. The acceleration due to gravity is g. Take the origin at the launch point. Suppose that y-axis is directed upward and speed v0 is in the x-direction. How long after you launch the potato has it moved as far horizontally from the launch point as it has moved vertically

Answer 1

Answer:

$\displaystyle t=\frac{2v_o}{g}$

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:

$\displaystyle y=\frac{gt^2}{2}$

The horizontal distance is

$x=v_ot$

We need to find the time when both distances are equal, thus

$\displaystyle \frac{gt^2}{2}=v_ot$

Simplifying by t

$\displaystyle \frac{gt}{2}=v_o$

Solving for t

$\displaystyle \boxed{t=\frac{2v_o}{g}}$