IIT PHYSICS – LESSON 3
MOTION IN A PLANE
STAGE–3 : JEE MAIN & JEE ADVANCED MATERIAL
🌟 Why Motion in a Plane is Important for IIT
This chapter introduces vector mechanics, which is the backbone of entire Mechanics. IIT questions test not memory, but vector reasoning and geometry.
1️⃣ Vectors – Mathematical Treatment
A vector is represented by an arrow. Its magnitude is the length of the arrow and direction is given by its orientation.
In Cartesian form:
Vector A = Ax î + Ay ĵ
Magnitude of vector:
|A| = √(Ax2 + Ay2)
2️⃣ Resolution of Vectors
Any vector can be resolved into perpendicular components.
If a vector A makes an angle θ with x-axis:
- Ax = A cosθ
- Ay = A sinθ
3️⃣ Projectile Motion (IIT Perspective)
Projectile motion is two-dimensional motion under constant gravity.
- Horizontal acceleration = 0
- Vertical acceleration = g (downward)
Equations of motion:
- x = u cosθ · t
- y = u sinθ · t − ½gt²
Trajectory equation:
y = x tanθ − (g x²) / (2u² cos²θ)
4️⃣ Important Results (Very High Weightage)
- Time of flight, T = (2u sinθ) / g
- Maximum height, H = (u² sin²θ) / (2g)
- Range, R = (u² sin2θ) / g
5️⃣ Relative Velocity (Vector Approach)
Relative velocity of A with respect to B:
vAB = vA − vB
Relative velocity problems are solved using:
- Vector subtraction
- Triangle law of vectors
- Parallelogram law
6️⃣ JEE MAIN Level Questions
Q1: A projectile is thrown with velocity 20 m/s at 30°. Find its time of flight.
Solution:
T = (2u sinθ)/g
= (2 × 20 × 0.5) / 10 = 2 s
Q2: Find the magnitude of vector having components (3î + 4ĵ).
Answer:
|A| = √(3² + 4²) = 5
7️⃣ JEE ADVANCED Thinking Problem
Q: Two particles are projected simultaneously from same point with same speed but at angles θ and (90° − θ). Compare their ranges.
Answer:
Ranges are equal, because sin2θ = sin[2(90° − θ)].
⚠️ Common IIT Mistakes
- Forgetting vector direction
- Wrong resolution of components
- Using scalar formulas for vector quantities
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