2026-03-09 05:57

Status: #new

Tags: #physic

2-D Kinematics

Composition Method

• Composition Method outlines a method that takes calculations of x and y values separately, all connected through the concept of time :O.
• Here's how it can be done:
  • The initial velocity ($\overrightarrow{v_i}$) of object x is A m/s at 30 degrees.
  • We can identity the x and y components through cosine and sine.
    • $\overrightarrow{v_{i_x}}$ = $\overrightarrow{v_i}cos({30}^{\circ })$
    • $\overrightarrow{v_{i_y}}$ = $\overrightarrow{v_i}sin({30}^{\circ })$
  • In addition, this can also be applied to the concept of acceleration
    • If we know that $\overrightarrow{v_{f_x}}$ = C m/s, then it can be inferred that a $\overrightarrow{v_{f_x}}$ = $\overrightarrow{v_{i_x}}+\overrightarrow{a_x}\mathrm{\Delta }t$
    • The same can concur for y: $\overrightarrow{v_{f_y}}$ = $\overrightarrow{v_{i_y}}+\overrightarrow{a_y}\mathrm{\Delta }t$
  • Notice that theres no degrees in the x and y sections?
    • Thats the power of composition, which enables this
• Calculating Acceleration and Pythagoras
  • If we can calculate only $\overrightarrow{a_x}$ or $\overrightarrow{a_y}$ , then we are severely limited. Theres a easy way to deal with this however...
    • $\overrightarrow{a}=\sqrt{\overrightarrow{a_x}+\overrightarrow{a_y}}[{\theta }_a]$ given that $[{\theta }_a]=ta{n}^{-1}(\frac{\overrightarrow{a_y}}{a_x})$
  • This concept can be applied to ALL of kinematics!

X and Y Tables

• Now that we have a mechanism to determine x and y and how to fuse them together, now we need an organized method of organizing those x and y's:
  • Given that say these two velocity vectors are the only vectors in our problem, using the pythagorean theorem method used in acceleration (see above)
    • We can determine the resultant velocity vector

Subtraction of Vectors

• We know that $\overrightarrow{a}=\frac{\overrightarrow{v_f}-\overrightarrow{v_i}}{\mathrm{\Delta }t}$
  • If we want to take the X and Y tables, we will have to subtract??. Now thats confusing. Hence we rewrite say -12cos(100) as + (-12cos100)
    • This leads to + (12cos280) or heck even + (12cos10)
  • Really, thats all there is to it:
    • Takeaway: (Vectors can be added and subtracted)

Projectile Motion

• In Projectile motions, we can always assume that the horizontal acceleration DNE. This implies that there is a constant horizontal motion. The real calculations occur with the vertical motion. Time links up the x and y components.
  • Acceleration is always calculated given $g=-9.8m/s^2$ where "-" represents a downward vertical motion
  • There are also a few adapted formulas and some key takeaways that can be observed:
• Greatest Maximums
  • A greatest maximum is defined by
    • $h_{max}=\frac{\overrightarrow{v_{yi}}}{19.6}$

References