A stone is thrown horizontally from an initial height h and hits the level groun

Question

A stone is thrown horizontally from an initial height h and hits the level ground at a horizontal distance of x from the starting point. Air resistance is small enough to ignore. A) Derive a formula for the initial speed of the stone. B) Derive a formula for the final speed of the stone as it hits the ground. Your derivations should include a clear statement or diagram, showing where you have placed the origin of your coordinate system and which direction(s) you have chosen as positive. For both parts A and B, simplify your final answer as much as possible.

Explanation / Answer

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he equations for rectilinear motion can be derived from the first principle.

Let us assume that an object starts with an initial velocity U and with a constant acceleration a. A simple calculation tells us that after a timet, the increase in velocity during that time t is acceleration × time, that is just at. Since the object already had an initial velocity u at the start, the quantity is also added to the increase in the velocity to determine the actual final velocity v.
In other words, the first equation for final velocity is framed as,

v = u + at

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