LESSON–3 : MOTION IN A PLANE

ADDITIONAL MATERIALS
IMPORTANT PROBLEMS + SMART TRICKS

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🔹 PART–A : IMPORTANT PROBLEMS (10)

Problem 1: Find the magnitude of a vector having components 6î + 8ĵ.

Answer:

|A| = √(6² + 8²) = √100 = 10

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Problem 2: A vector of magnitude 20 m/s makes an angle of 30° with horizontal. Find its horizontal component.

Answer:

v_x = v cosθ = 20 × cos30° = 17.32 m/s

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Problem 3: Find the vertical component of velocity 25 m/s at 60°.

Answer:

v_y = v sinθ = 25 × sin60° = 21.65 m/s

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Problem 4: A projectile is thrown with speed 10 m/s at 45°. Find its time of flight. (g = 10 m/s²)

Answer:

T = (2u sinθ)/g
= (2 × 10 × sin45°)/10 = 1.41 s

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Problem 5: Find the maximum height of a projectile thrown at 30° with speed 20 m/s.

Answer:

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

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Problem 6: Find the range of a projectile thrown at 45° with speed 20 m/s.

Answer:

R = (u² sin2θ)/g
= (400 × 1)/10 = 40 m

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Problem 7: 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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Problem 8: A body is projected horizontally with velocity 10 m/s. Find the horizontal distance travelled in 3 s.

Answer:

Distance = u × t = 10 × 3 = 30 m

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Problem 9: Two trains move in opposite directions with speeds 40 km/h and 60 km/h. Find relative velocity.

Answer:

Relative velocity = 40 + 60 = 100 km/h

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Problem 10: At the highest point of projectile motion, what is the velocity?

Answer:

Only horizontal component exists. Vertical component is zero.

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🔹 PART–B : SMART TRICKS & SHORTCUTS

🎯 Trick 1: Resolve First, Think Later

In any vector or projectile problem, first resolve velocity into horizontal and vertical components.

🎯 Trick 2: Remember Three Golden Formulas

• T = (2u sinθ)/g
• H = (u² sin²θ)/(2g)
• R = (u² sin2θ)/g

🎯 Trick 3: Complementary Angles

Projectiles fired at θ and (90° − θ) have equal range.

🎯 Trick 4: Horizontal Projection Rule

Horizontal motion is uniform. Vertical motion is free fall.

🎯 Trick 5: Relative Velocity Shortcut

• Same direction → subtract speeds
• Opposite direction → add speeds

🎯 Trick 6: Highest Point Logic

At highest point:

• Vertical velocity = 0
• Acceleration ≠ 0 (still g)

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🏆 FINAL LEARNING TIP

If you master these 10 problems and tricks, Motion in a Plane becomes a scoring chapter in both Intermediate and IIT exams.