LESSON–3 : MOTION IN A PLANE

ADDITIONAL MATERIALS – 9
IIT JEE PREVIOUS YEAR QUESTIONS & ANSWERS
(Method • Tricks • Problem Solving Procedure)

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🔹 PYQ–1 (JEE ADVANCED – METHOD BASED)

Question:
At the highest point of a projectile, find the direction and magnitude of velocity and acceleration.

Answer:

Velocity → Horizontal only (v = u cosθ)
Acceleration → Vertically downward (g)

Method & Trick:

• Always separate velocity into horizontal and vertical components
• At highest point → v_y = 0 (NOT acceleration)

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🔹 PYQ–2 (JEE MAIN – TIME METHOD)

Question:
A stone is projected horizontally from a cliff. Another stone is dropped from the same point. Which reaches the ground first?

Answer:

Both reach the ground at the same time.

Problem Solving Procedure:

1. Identify vertical motion
2. Use equation: h = ½gt²
3. Horizontal velocity does not affect time

Shortcut Trick:

Time of fall depends ONLY on height and gravity.

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🔹 PYQ–3 (JEE ADVANCED – RANGE LOGIC)

Question:
Two projectiles are projected with the same speed at angles θ and (90°−θ). Compare their ranges.

Answer:

Ranges are equal.

Method:

• Use range formula: R = (u² sin2θ)/g
• sin(2θ) = sin[2(90°−θ)]

Smart Trick:

Complementary angles → Same range (remember without calculation)

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🔹 PYQ–4 (JEE ADVANCED – VECTOR METHOD)

Question:
Find the angle between vectors A = 3î + 4ĵ and B = 4î − 3ĵ.

Answer:

Dot product = 3×4 + 4×(−3) = 0
Angle = 90°

Solving Procedure:

1. Use dot product formula
2. If dot product = 0 → vectors are perpendicular

Trick:

(a, b) and (b, −a) are always perpendicular.

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🔹 PYQ–5 (JEE MAIN – SPEED COMPARISON)

Question:
Compare speed of a projectile at projection and at landing (same level).

Answer:

Speeds are equal.

Method:

• Use energy conservation
• Height difference = 0

Shortcut:

Same level → Same speed (no need of calculation)

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🔹 PYQ–6 (JEE ADVANCED – RELATIVE VELOCITY)

Question:
Two bodies move perpendicular to each other with speeds 20 m/s and 15 m/s. Find their relative speed.

Answer:

Relative speed = √(20² + 15²) = 25 m/s

Procedure:

1. Check angle between velocities
2. Perpendicular → use Pythagoras theorem

Trick:

Perpendicular velocities → √(v₁² + v₂²)

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🔹 PYQ–7 (JEE ADVANCED – ZERO ACCELERATION TRAP)

Question:
Is acceleration of a projectile zero at the highest point?

Answer:

No. Acceleration is always equal to g and acts downward.

Concept Check:

• Velocity can be zero (component)
• Acceleration NEVER becomes zero

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🔹 PYQ–8 (JEE MAIN – TIME RATIO)

Question:
Find the ratio of time taken to reach maximum height to total time of flight.

Answer:

Ratio = 1 : 2

Trick:

Projectile motion is symmetric about highest point.

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🔹 PYQ–9 (JEE ADVANCED – FINAL LOGIC)

Question:
Can velocity and acceleration of a projectile ever be perpendicular?

Answer:

Yes, at the highest point.

Logic:

• Velocity → horizontal
• Acceleration → vertical

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🔹 PYQ–10 (JEE ADVANCED – THINK FIRST)

Question:
Which quantity remains constant throughout projectile motion?

Answer:

Horizontal component of velocity.

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🧠 MASTER PROBLEM SOLVING FRAMEWORK (VERY IMPORTANT)

1. Draw a rough diagram
2. Resolve velocity into x and y components
3. Apply equations separately for x and y motions
4. Use symmetry and energy conservation
5. Check physical meaning of answer

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✅ ADDITIONAL MATERIALS – 9 COMPLETED
(Methods + Tricks + Solving Procedures)