LESSON–3 : MOTION IN A PLANE

ADDITIONAL MATERIALS – 3
IIT JEE PREVIOUS YEAR QUESTIONS & ANSWERS

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🔹 PYQ–1 (JEE MAIN)

Question:
A projectile is projected with velocity 20 m/s at an angle of 30°. Find its maximum height. (g = 10 m/s²)

Answer:

H = (u² sin²θ) / (2g)
= (400 × 0.25) / 20
= 5 m

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🔹 PYQ–2 (JEE MAIN)

Question:
Find the magnitude of vector A = 3î + 4ĵ.

Answer:

|A| = √(3² + 4²) = 5

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🔹 PYQ–3 (JEE MAIN)

Question:
Two particles move with velocities 10î + 2ĵ and 4î − 2ĵ. Find the relative velocity of first particle with respect to second.

Answer:

v_AB = (10 − 4)î + (2 + 2)ĵ
= 6î + 4ĵ

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🔹 PYQ–4 (JEE ADVANCED)

Question:
At the highest point of a projectile, which of the following is zero?
(a) Velocity
(b) Acceleration
(c) Vertical component of velocity
(d) Horizontal component of velocity

Answer:

Correct option: (c) Vertical component of velocity

Acceleration is not zero; it is always g downward.

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🔹 PYQ–5 (JEE ADVANCED)

Question:
A projectile is projected at angle θ with horizontal. At what angle will its range be maximum?

Answer:

Range R = (u² sin2θ)/g
Maximum when sin2θ = 1
⇒ 2θ = 90°
⇒ θ = 45°

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🔹 PYQ–6 (JEE ADVANCED – CONCEPTUAL)

Question:
Can the velocity of a projectile ever be perpendicular to its acceleration?

Answer:

Yes. At the highest point, velocity is horizontal and acceleration is vertical.

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🔹 PYQ–7 (JEE MAIN)

Question:
Two projectiles are thrown with same speed at angles 30° and 60°. Compare their ranges.

Answer:

Ranges are equal because:
sin60° = sin120°

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🔹 PYQ–8 (JEE ADVANCED)

Question:
A projectile is projected horizontally from the top of a tower. Which quantity remains constant during motion?

Answer:

Horizontal component of velocity remains constant.

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🔹 PYQ–9 (JEE MAIN)

Question:
A particle moves with velocity v = 2î + 3ĵ. Find its speed.

Answer:

Speed = √(2² + 3²) = √13 m/s

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🔹 PYQ–10 (JEE ADVANCED – THINKING)

Question:
Two bodies are projected simultaneously from the same point, one vertically upward and the other horizontally with same speed. Which one hits the ground first?

Answer:

Both hit the ground at the same time, because time depends only on vertical motion.

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🎯 PYQ SOLVING STRATEGY

• Always draw a rough diagram first
• Resolve velocity into components
• Use symmetry and complementary angle logic
• Do not memorise blindly – understand motion

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✅ ADDITIONAL MATERIALS – 3 (IIT PYQs) COMPLETED