LESSON–3 : MOTION IN A PLANE

ADDITIONAL MATERIALS – 2
ADVANCED PROBLEMS + THINKING TRICKS

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🔹 PART–A : ADVANCED PRACTICE PROBLEMS (10)

Problem 1: A vector has components 5î − 12ĵ. Find its magnitude.

Answer:

|A| = √(5² + 12²) = √169 = 13

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Problem 2: Find the angle made by vector 3î + √3 ĵ with x-axis.

Answer:

tanθ = (√3) / 3
θ = 30°

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Problem 3: A projectile is thrown with velocity 20 m/s at 60°. Find its time of flight. (g = 10 m/s²)

Answer:

T = (2u sinθ)/g
= (2 × 20 × sin60°)/10
= 3.46 s

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Problem 4: Find the maximum height reached by the projectile in Problem–3.

Answer:

H = (u² sin²θ)/(2g)
= (400 × 3/4) / 20 = 15 m

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Problem 5: Two projectiles are projected with same speed. One at 30° and the other at 60°. Which one stays longer in air?

Answer:

Time of flight ∝ sinθ
Since sin60° > sin30°, 60° projectile stays longer.

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Problem 6: A body is projected horizontally from a tower of height 45 m. Find the time taken to reach the ground. (g = 10 m/s²)

Answer:

h = ½gt²
45 = 5t²
t = 3 s

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Problem 7: Find the horizontal distance covered in Problem–6 if horizontal velocity is 10 m/s.

Answer:

Distance = u × t = 10 × 3 = 30 m

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Problem 8: Two cars move perpendicular to each other with speeds 20 m/s and 15 m/s. Find the magnitude of relative velocity.

Answer:

Relative velocity = √(20² + 15²)
= √625 = 25 m/s

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Problem 9: At what angle should a projectile be thrown to get maximum range?

Answer:

45°

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Problem 10: What is the acceleration of a projectile at the highest point?

Answer:

Acceleration = g downward
It is not zero.

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🔹 PART–B : ADVANCED THINKING TRICKS

🎯 Trick 1: Time of Flight Depends Only on Vertical Motion

Horizontal velocity does not affect time of flight. Only vertical component decides it.

🎯 Trick 2: Use sinθ Logic Instead of Formula

If speed is same:

• Higher angle → more time in air
• Lower angle → less time in air

🎯 Trick 3: Complementary Angle Shortcut

Angles θ and (90° − θ):

• Same range
• Different time of flight

🎯 Trick 4: Perpendicular Velocities

If velocities are perpendicular:

Resultant = √(v₁² + v₂²)

🎯 Trick 5: Highest Point Rule

At highest point:

• Vertical velocity = 0
• Horizontal velocity ≠ 0
• Acceleration always acts downward

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🏆 FINAL PRACTICE ADVICE

If you solve **Additional–1 + Additional–2** fully, you will be able to handle any Intermediate-level problem and many IIT-level basic problems from this chapter.