Horizontal Projectile Motion (Class 11, 12, NEET/JEE)

Aapne kabhi table se coin ko slide karke girte dekha hai? Ya kisi cliff se seedha patthar ko horizontal direction me phenka ho?
Jo path wo follow karta hai — wahi hai Horizontal Projectile Motion.

Horizontal Projectile Motion Kya Hota Hai?

Jab koi object ko sirf horizontal direction me velocity dekar chhoda jata hai, aur uske baad us par sirf gravity ka effect hota hai, to us motion ko horizontal projectile motion kehte hain.

• Initial vertical velocity = 0
• Sirf gravity vertical direction me kaam karti hai
• Path hamesha parabolic hota hai

Real life examples:

• Table se girta hua ball
• Cliff se phenka gaya stone
• Aeroplane se girta packet

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Motion Ko 2 Parts Me Tod Do (Golden Trick)

Projectile ko samajhne ka sabse powerful tareeka:

Horizontal aur Vertical motion ko alag-alag treat karo

Direction	Kya ho raha hai?	Formula
Horizontal (x)	Uniform motion (no acceleration)	$x = ut$
Vertical (y)	Free fall (gravity)	$y = \tfrac{1}{2}gt^2$y

Yahi trick 90% questions solve kara deti hai.

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Diagram Socho (Mind Sketch)

Mind me ye diagram bana lo:

• Object table ke edge se nikalta hai
• Neeche gravity kheech rahi hai
• Aage constant speed se ja raha hai
• Path = parabola

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Step-by-Step Derivation (Bahut Easy Way)

Maan lo object height h se horizontal speed u se nikla.

Step 1 — Time of Flight (sabse pehle ye nikalo)

Vertical motion use karo:$$h = \tfrac{1}{2}gt^2$$$$t = \sqrt{\tfrac{2h}{g}}$$

Notice: Time me ‘u’ nahi aaya — kyunki vertical me u = 0

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Step 2 — Horizontal Range (kitna door gira)

Horizontal motion:$$R = u \times t$$$$R = u \sqrt{\tfrac{2h}{g}}$$

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Step 3 — Trajectory Equation (path ka equation)

Horizontal: $x = ut \Rightarrow t = \tfrac{x}{u}$x=ut⇒t=ux​

Vertical me put karo:$$y = \tfrac{1}{2}g\left(\tfrac{x}{u}\right)^2$$$$y = \tfrac{g}{2u^2}x^2$$

Ye parabola ka equation hai.

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Important Observations (Exam Gold Points)

1. Time of flight speed par depend nahi karta
2. Zyada speed doge → object zyada door jayega
3. Har horizontal projectile ka path parabola hota hai
4. Vertical motion free fall jaisa hota hai

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Real Life Example:

Socho ek aeroplane seedha ja raha hai aur usme se ek packet giraya.

Packet:

• Plane ke saath aage badhta rahega
• Saath hi neeche girta rahega
• Ground par plane ke neeche nahi, balki aage jaake girega

Yahi concept exams me pucha jata hai.

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Solved Example (NEET/JEE Level)

Question:
Ek ball ko 20 m height wali table se 10 m/s speed se horizontal throw kiya. Range nikalo. (g = 10)

Step 1: Time$$t = \sqrt{\tfrac{2h}{g}} = \sqrt{\tfrac{40}{10}} = 2 \text{ s}$$t=g2h​​=1040​​=2 s

Step 2: Range$$R = ut = 10 \times 2 = 20 \text{ m}$$R=ut=10×2=20 m

Bas. 2 steps. Khatam.

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Common Mistakes Students Karte Hain

• Vertical me $u$u laga dete hain (galat)
• Dono motions ko mix kar dete hain
• Time nikaale bina range nikalne ki koshish
• Diagram nahi banate

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Previous Year Question Patterns (NEET/JEE)

• Time of flight poochna
• Range poochna
• Trajectory equation
• Do balls: ek drop, ek horizontal throw — kaun pehle girega?

Answer: Dono same time me girenge.

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Quick Revision Formula Sheet

Quantity	Formula
Time of flight	$t = \sqrt{2h/g}$t
Range	$R = u\sqrt{2h/g}$
Trajectory	$y = \tfrac{g}{2u^2}x^2$

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Concept Check (Aapse Sawal)

1. Agar speed double kar dein to time pe kya effect?
2. Agar height double ho jaye to time?
3. Kya horizontal projectile me acceleration hoti hai?

(Answers: No change, increases, only vertical)

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Final Summary (Ratta Nahi, Samajh Lo)

Horizontal me uniform motion
Vertical me free fall
Dono ko alag treat karo → 90% question solved

Ye topic dikhne me chhota hai, par NEET/JEE me bahut favourite hai.

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