<p>I dont understand why a object projected horizontally and an object dropped vertically reach the lowest point in the same time. Of course, I can just blindy recognize this Galilean principle and hope that a teacher doesnt approach me with a question asking me to explain how this works, but it annoys me that i dont understand the mathematical principles which actually prove why this happens.</p>
<p>so, um, are you just saying you want someone to explain it clearly how it works to you?</p>
<p>Uhm, I didn’t quite get question but what are surroundings? There is no gravitation, right?</p>
<p>i’m assuming some background in basic physics</p>
<p>suppose we have some gravitational field of strength g. assuming the objects aren’t acted upon by air resistance/friction/any other forces, we can assume the vertical acceleration of the objects is constant and equal to g.</p>
<p>decompose all forces acting on the objects into horizontal and vertical components. since gravity acts downwards, its force has horizontal component equal to zero. since no other forces besides gravity act on the objects, there is no horizontal acceleration. </p>
<p>but all we care about is the vertical displacement of the objects, we can see that their behavior in the vertical direction is identical, regardless of the initial horizontal velocity of one of the objects.</p>
<p>so, they will cover the same vertical distance in the same amount of time. quantitatively, using the constant acceleration kinematics equations, the time required to fall a distance h is sqrt(2h/g).</p>
<p>The horizontal motion of the object is trivial here. It could even be accelerated or decelerated by a horizontal force.</p>
<p>We’re only concerned with its vertical motion. Near Earth we know that all objects are accelerated by this thing called gravity at a constant rate of g = 9.8 m/s^2. Now, if two objects have the same vertical motion initially (same position, same velocity), they will fall the same amount in equal times, for they are accelerating (the only other factor determining position) at the same amount, as well.</p>
<p>In science, for us we don’t use decelerate. There are different factors you need to list, be specific. Gravity is constant so initial velocity/velocity would always equadistant. In an ideal situation, all objects dropped from the same height will land at the same time. Gravity causes the same acceleration for everything. Gravity pulls down on an object. The object’s mass resists the pull. This resistance is called inertia. In an ideal situation the heavier object gets pulled harder, but resists harder as well. Both the heavier and lighter
object therefore move the same way. Remember on the moon dropping an object anywhere will have the same landing times.</p>
<p>A simple way to put it.</p>
<p>The simplest way to explain it is, quite simply, that motion in the horizontal direction does not effect motion in the vertical. This means the horizontal direction of something (ie a speeding bullet or something falling straight down) doesn’t make a difference- it’s just the speeding bullet will probably hit something first so you won’t see it drop to the ground!</p>
<p>um yes yes yes i know i dont know what evea is goof but play video games</p>