I am supposed to write a paper, about a page long, about projectile motion. How would I go about this? Oh and by the way, it is about projectile motion in context of soccer.
Instructions given to me:
-1 page report with 3 sections:
---Introduction explaining/defining your topic – no more than ¼ of the page
---Body describing your thoughts and ideas on how the topic applies to soccer - ~1/2 page
---Conclusion/wrapup – no more than ¼ of the page

Question

I am supposed to write a paper, about a page long, about projectile motion. How would I go about this? Oh and by the way, it is about projectile motion in context of soccer.
Instructions given to me:
-1 page report with 3 sections:
---Introduction explaining/defining your topic – no more than ¼ of the page
---Body describing your thoughts and ideas on how the topic applies to soccer - ~1/2 page
---Conclusion/wrapup – no more than ¼ of the page

jmartinez638 · Answer

I know this isn't a physics problem per se, but a little help would be appreciated.

michele_laino · Answer

the best way in order to describe a motion of a projectile, is to provide the involved vector equations

jmartinez638 · Answer

Ok, that makes sense.

michele_laino · Answer

are you familiar with vector calculus?

jmartinez638 · Answer

I'm in AP Calc, so yes.

michele_laino · Answer

In general the motion of a projectile produces a parabolic trajectory, of course, if we can neglect the friction due to the surrounding air

michele_laino · Answer

furthermore, we can consider such motion, as a motion which occurs inside a geometric plane, namely the motion of a projectile, can be described using only two coordinates, for example $x,z$

michele_laino · Answer

more precisely:
$\large x$ is the horizontal coordinate, and $ \large z$ is the vertical coordinate

michele_laino · Answer

with such framework we can make this drawing:
|dw:1446033957410:dw|
where the vector ${\mathbf{g}}$ represents gravity, and we can write:
$$\Large  {\mathbf{g}} = \left( {0, - g} \right)$$
where: $$\Large g = 9.81\;m/{\sec ^2}$$

jmartinez638 · Answer

That definitely makes sense.

michele_laino · Answer

now, starting from this equation: $$\Large {\mathbf{g}} = \left( {0, - g} \right)$$ we can write the parabolic trajectory.

michele_laino · Answer

please wait a moment, I have to answer to my phone

michele_laino · Answer

ok! I'm here

michele_laino · Answer

using the rules of differential calculus, we get the subsequent formula which describes the trajectory of a projectile:
$$\Large   z\left( x \right) = x\tan \theta  - \frac{{g{x^2}}}{{2v_0^2{{\left( {\cos \theta } \right)}^2}}}$$
where $\Large  v_0$ is the magnitude of the initial velocity of the projectile, and $\Large \theta$ is the angle as |dw:1446035361871:dw|below:

michele_laino · Answer

here is the parabolic trajectory:
|dw:1446035463936:dw|