Foundations — Projectile motion — horizontal - vertical independence, full derivation

1.1.19 · D1 · Physics › Measurement, Vectors & Kinematics › Projectile motion — horizontal - vertical independence, full

Yeh page ek toolbox unpacking hai. Parent note (Projectile motion — horizontal - vertical independence, full derivation) mein $\vec{F}$, $u\cos \theta$, $a_y=-g$, aur $\int vdt$ jaise symbols aise use hote hain jaise tumhe pehle se pata ho. Yahan hum har ek ko earn karte hain, build-order mein, ek picture ke saath.

1. Position, origin, aur axes ($x$, $y$, $O$)

Figure dekho: $O$ bottom-left corner hai. Dot par baitha hua ball do numbers se describe hota hai — $x$ daayein chalo, phir $y$ upar. Woh do numbers hi uski position hain.

2. Time $t$ — shared clock

Hum $x(t)$ aur $y(t)$ likhte hain — padho "$x$ at time $t$" — yeh emphasize karne ke liye ki position time ki ek function hai: mujhe $t$ do, main tumhe position wapas dunga.

3. Velocity — ek arrow jiski length aur direction hai

4. Launch angle $\theta$

Agla figure dekho: amber arrow length $u$ ki launch velocity hai, ground line se $\theta$ upar tilt kiya hua.

5. Arrow ko split karna: $\sin \theta$, $\cos \theta$, aur components

Yeh single most important tool hai jo parent assume karta hai. Hum ise dheere-dheere banate hain.

Usi figure mein cyan dashed lines yeh do sides dikhati hain. Sideways shadow $u_x$ hai; vertical shadow $u_y$ hai.

Split ke har case

6. Acceleration $a$ aur gravity $g$

Dono directions yahan perfectly split hote hain: $a_x=0(\text{koi sideways push nahin}),a_y=-g(\text{gravity, downward}).$

7. Force $\vec{F}$ aur Newton's law, component by component

8. Slicing tools: $\frac{dv}{dt}$ aur $\int vdt$

Parent likhta hai $a=\frac{dv}{dt}$ aur $x=\int vdt$. Yahan woh squiggles ka matlab hai, zero se.

Agar constant acceleration comfortable lage ready-made formulas ke roop mein (no calculus), algebraic route $v=u+at$, $s=ut+\frac{1}{2}a{t}^2$ 1-D Kinematics — Equations of Motion mein hai — yeh wahi result hai jo integration produce karta hai.

9. Parabola aur $\tan \theta$

Prerequisite map

Ise top-to-bottom padho: left/top par raw ideas parametric equations $x(t),y(t)$ ko feed karte hain, aur woh badle mein har woh result dete hain jo parent box karta hai.

Equipment checklist

Daayein side cover karo aur khud test karo — jab har ek instant ho tab tum full derivation ke liye ready ho.