LESSON–3 : MOTION IN A PLANE

ADDITIONAL MATERIALS – 6
IIT JEE PREVIOUS YEAR QUESTIONS & ANSWERS (SET–4)

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🔹 PYQ–1 (JEE ADVANCED – MINIMUM SPEED)

Question:
At which point of a projectile’s path is its speed minimum?

Answer:

Speed is minimum at the highest point, because vertical component of velocity becomes zero.

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🔹 PYQ–2 (JEE MAIN – VECTOR RESULTANT)

Question:
Two vectors of magnitudes 5 and 12 act perpendicular to each other. Find the magnitude of their resultant.

Answer:

Resultant = √(5² + 12²) = √169 = 13

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🔹 PYQ–3 (JEE ADVANCED – TIME LOGIC)

Question:
A stone is projected horizontally from the top of a tower. Another stone is dropped vertically from the same height at the same time. Which stone reaches the ground first?

Answer:

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

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🔹 PYQ–4 (JEE ADVANCED – VELOCITY DIRECTION)

Question:
At what point does the velocity of a projectile make the smallest angle with the horizontal?

Answer:

At the highest point, because vertical component becomes zero.

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🔹 PYQ–5 (JEE MAIN – HEIGHT CALCULATION)

Question:
A projectile is thrown with speed 50 m/s at an angle of 30°. Find the maximum height reached. (g = 10 m/s²)

Answer:

H = (u² sin²θ)/(2g)
= (2500 × 0.25)/20
= 31.25 m

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🔹 PYQ–6 (JEE ADVANCED – ACCELERATION TEST)

Question:
Is the acceleration of a projectile ever zero during its flight?

Answer:

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

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🔹 PYQ–7 (JEE MAIN – RELATIVE VELOCITY)

Question:
Two particles move with velocities (7î + 24ĵ) m/s and (1î + 6ĵ) m/s. Find the magnitude of relative velocity.

Answer:

v_AB = (6î + 18ĵ)
|v_AB| = √(36 + 324) = √360 = 6√10 m/s

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🔹 PYQ–8 (JEE ADVANCED – ENERGY VIEW)

Question:
A projectile is projected from ground level. Compare the kinetic energies at the point of projection and at the point of landing.

Answer:

Kinetic energies are equal, because speed at projection and landing are equal.

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🔹 PYQ–9 (JEE MAIN – VECTOR ANGLE)

Question:
Find the angle made by vector (8î + 6ĵ) with x-axis.

Answer:

tanθ = 6 / 8 = 3 / 4
θ = 36.9°

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🔹 PYQ–10 (JEE ADVANCED – CORE CONCEPT)

Question:
Can the velocity of a projectile ever be zero during its motion?

Answer:

No. At the highest point, only the vertical component becomes zero, but horizontal component always exists.

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🎯 ELITE JEE SOLVING STRATEGY

• Always separate horizontal and vertical motions
• Do not assume acceleration becomes zero
• Use energy conservation to save time
• Check extreme cases (highest point, landing point)
• Think physically, not mechanically

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✅ ADDITIONAL MATERIALS – 6 (IIT PYQs) COMPLETED