Vertical motion is basically the same as horizontal motion; you use the same
formulas, it has the same variables, etc. The main difference though is that vertical
motion involves gravity. That might sound intimidating, but actually, it makes things
easier. The only thing it means is that in every vertical motion problem you do
involving earth, your accelleration will always be -9.8m/s2. It's a free-be, just one
less thing for you to worry about.
In this first lesson, we will work with objects that are dropped, meaning that vo
is 0m/s. The next lesson will cover situations where objects have initial velocities
other than 0m/s.
As stated earlier, for vertical motion you use the same equations as you do for
horizontal. Be careful though not to combine horizontal and vertical variables into the
same equation. The equations will work for the two different types of motion, but the
horizontal and vertical portions must remain separate, just like the horizontal and
vertical components must remain separate when working with vectors.
Since there are no new equations, and the only thing we added was the fact that now
acceleration will always equal -9.8m/s2, let's work a sample problem.
A penny is dropped off a tall building and hits the ground 5 seconds later.
a. How tall is the building?
b. What was the impact velocity of the penny on the ground?
For part a, let's use one of the new substitution equations we learned in the last
lesson. d = vot + 0.5*a*t2
d = 0m/s*5s + 0.5*(-9.8m/s2)*(5s)2
d = -122.5m
Since height is a scalar, meaning it doesn't have direction, we can take off the (-)
leaving us with a height of 122.5m.
We don't even need to use one of the substitution equations for part b, all we need
is the acceleration formula. a = (vf - vo) / t
-9.8m/s2 = (vf - 0m/s) / 5s
-49m/s = vf
Now, since velocity is not a scalar, it is a vector and therefore has direction, we
leave the (-) on giving us -49m/s as the final velocity. Since this is a vertical
motion problem the (-) lets us know that it is going down. Later on though when working
with motion that is a combination of vertical and horizontal, we will need to specify
the exact angle at which the object is going.
Objects with initial velocities other than 0m/s will be covered in the
next lesson.
