# I don't understand about free fall and its dependency on mass?

I am a 9th grade student. I study about free fall, and I got very confuse. I have a couple of questions about it.

I learn two formulas of free fall,

$$h=(1/2)gt^2$$

$$v=gt$$

From the height formula, the time object takes to fall to the ground don't depend on its mass. But I don't understand why when I drop a marker and a paper, the marker always fall to the ground first. I think that is because the marker is more massive than the paper, but why doesn't the formula has mass?

I hear a story about a penny drops from a very high building can kill people if it drop on people's head. I think it maybe because due to the height, the penny takes a long time to fall. And since velocity is promotional to time, the penny will have a large velocity when it land on top of people. So, is this true? Can penny drops from high building can kill people on the ground?

• Wow! you really are confusing about the freefall motion. The problem is the example you are giving is not exactly a freefall motion. I don't think you understand what freefall motion is.
– TBBT
Oct 22, 2016 at 15:02
• I am. I don't understand my teacher much. Can you help me?
– user133882
Oct 22, 2016 at 15:11
– TBBT
Oct 22, 2016 at 15:22
• Related: physics.stackexchange.com/q/11321/2451 and links therein. Oct 22, 2016 at 15:24
• I read this post and other like it, but it doesn't help me to answer my questions above.
– user133882
Oct 22, 2016 at 15:32

The same thing happens to the penny falling through the air. Once it reaches a certain speed or "terminal velocity", it can't go any faster. So, it continues to fall in a constant speed until it hits the ground. The terminal velocity of the penny is around $40km/h$ after falling for about $15m$.
Now, when penny or any other objects that are "supposedly" drop on your head, the damage is not only depend on the velocity when it hits, but also the mass of the object. This is the concept of kinetic energy. Kinetic energy is given as $$K=\frac{1}{2}mv^{2}$$ When the penny hits you, its kinetic energy transfers to your head. Since penny is very light and not aerodynamic, it has little kinetic energy when it falls onto you. Other objects, depend on their mass and shape, can surely ruin your days if one drop on your head from high enough.