- Free-falling objects do not encounter air resistance.
- All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations)
The Physics of Free Falling Bodies
A common thread through almost all applications of physics is the concept of gravity and free falling bodies, which is simply the physical effect that causes objects to fall downward.
Physicists discovered that on earth objects fall towards the earth at a constant acceleration of 9.81 m/s2or 32.2 ft/s2. This is called the acceleration due to gravity and is typically identified with the symbol “g”. As with lots of things in physics, this is an “idealized” theory … that is, it is not 100% true … there are lots of situations and outside forces that impact the acceleration due to gravity including (but not limited to):
- air resistance
- distance above the earth
- latitude
- etc
But YOU need not worry about these cases. For our purposes we are always going to treat the acceleration due to gravity as though it is pure and constant. Why make things more complicated than they need to be, right?
1. Dropping Objects (V0 = 0)
When you “drop” an object it’s initial velocity is always zero . This is because before you drop it, the object is stationary in your hand.
2. Throwing or Shooting Objects Downward (V0 ≠ 0)
When you throw or shoot an object (a ball or an arrow or whatever) it’s initial velocity is NOT equal to zero. The object being thrown or shot leaves the point of departure with a certain velocity (which is either given or can be calculated from other info) and that speed is V0
3. Throwing or Shooting Objects Upward (Max Height is at V = 0 m/s)
When you throw or shoot something upward, it doesn’t go up forever, right? It goes up at a certain initial speed, slows down as it is rising (due to the effects of gravity) and then reaches a point where it stops and changes direction coming back down towards the Earth.
A common physics question is to ask “How high does the object go when thrown/shot upward?”. What they don’t outright tell you is that the maximum height of the object is the point where it stops and changes direction. That maximum height where the switch from going up to coming down happens … there is a split second where the object isn’t moving at all and THAT is where the maximum height is … where V = 0 m/s!
4. Objects that Go Upward Then Downward (Double Whammy: Time Up = Time Down, Speed at Start = Speed at End)
Personally, I think that assuming people understand this concept is quite unfair because I don’t think the average person realizes this throughout their normal existences in living with gravity. But, regardless of what I think, your physics textbook assumes this is common knowledge…
When you throw a ball up in the air it takes the same amount of TIME to go UP as it does to come DOWN.
Also, the speed at which the object is sent upwards (it’s initial velocity) will be the same speed at which it returns to that point (it’s final velocity).
Personally I found this concept a bit hard to believe until I though about it for a while.
The way I like to think about it is to round the acceleration due to gravity to 10 m/s2 just to make the math easy. Then I think through a problem.
Imagine I shot an arrow straight up at 20 m/s. At 0 seconds it would be going 20 m/s, then at 1 second it would be going 10 m/s (it loses 10 m/s per second), then at 2 seconds it would be going 0 m/s… at that point it would start heading back towards the Earth … so at 3 seconds it would be going 10 m/s again, then at 4 seconds 20 m/s and we’d be back where we began thus proving that the speed at which it was shot up at is the speed it will return at.
5. The COMBO (Dun-Dun-DUUUUN)
The last common scenario that comes up in physics problems is what I call the COMBO. This is when they take two (or more) of the concepts shown above and squish them together for your frustration 
For example, they may take the concept from 4 that we just went through above and add a CLIFF to it so that the point of return of the object is different than the point of release (ARG!) In these instances you usually have to solve the problem in two parts.
I know that students often fret about breaking a problem into parts …. DON’T FRET … even the experts do it and, in most cases it is the only way to solve the problem.
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