Chapter 4: Motion in a Plane
NCERT Solutions for CBSE Class 10 Physics — 105 solved questions with detailed explanations.
Solved Questions
Q1. Two vectors of magnitudes 3 and 4 are perpendicular to each other. The magnitude of their resultant is:
Difficulty: Easy · Topic: Vector Addition
Solution
R = √(3² + 4²) = √(9+16) = √25 = 5.
Q2. The range of a projectile is maximum when the angle of projection is:
Difficulty: Easy · Topic: Projectile Range
Solution
Range R = u²sin2θ/g. R is maximum when sin2θ = 1, i.e., 2θ = 90°, θ = 45°.
Q3. A projectile is fired at 30° to the horizontal with velocity 20 m/s. The maximum height reached is (g = 10 m/s²):
Difficulty: Easy-Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 400 × sin²30°/(2×10) = 400 × 0.25/20 = 5 m.
Q4. Two vectors of magnitudes 3 and 4 act at an angle of 90°. The magnitude of the resultant is:
Difficulty: Easy-Medium · Topic: Vector Addition
Solution
R = √(A²+B²+2ABcosθ) = √(3²+4²+2×3×4×cos90°) = 5.0.
Q5. Two vectors of magnitudes 5 and 12 act at an angle of 90°. The magnitude of the resultant is:
Difficulty: Easy-Medium · Topic: Vector Addition
Solution
R = √(A²+B²+2ABcosθ) = √(5²+12²+2×5×12×cos90°) = 13.0.
Q6. Two vectors of magnitudes 6 and 8 act at an angle of 90°. The magnitude of the resultant is:
Difficulty: Easy-Medium · Topic: Vector Addition
Solution
R = √(A²+B²+2ABcosθ) = √(6²+8²+2×6×8×cos90°) = 10.0.
Q7. Two vectors of magnitudes 3 and 4 act at an angle of 60°. The magnitude of the resultant is:
Difficulty: Easy-Medium · Topic: Vector Addition
Solution
R = √(A²+B²+2ABcosθ) = √(3²+4²+2×3×4×cos60°) = 6.08.
Q8. Two vectors of magnitudes 5 and 5 act at an angle of 60°. The magnitude of the resultant is:
Difficulty: Easy-Medium · Topic: Vector Addition
Solution
R = √(A²+B²+2ABcosθ) = √(5²+5²+2×5×5×cos60°) = 8.66.
Q9. Two vectors of magnitudes 10 and 10 act at an angle of 120°. The magnitude of the resultant is:
Difficulty: Easy-Medium · Topic: Vector Addition
Solution
R = √(A²+B²+2ABcosθ) = √(10²+10²+2×10×10×cos120°) = 10.0.
Q10. A particle moves in a circle of radius 10 cm with constant speed completing one revolution in 2 seconds. The magnitude of acceleration is:
- π² cm/s²
- 2π² cm/s²
- 4π² cm/s²
- 10π² cm/s²
Difficulty: Medium · Topic: Circular Motion
Solution
a = ω²r = (2π/T)² × r = (2π/2)² × 10 = π² × 10 = 10π² cm/s².
Q11. Rain is falling vertically with velocity 10 m/s. A man is walking with velocity 5 m/s. The angle at which he should hold his umbrella with respect to vertical is:
- tan⁻¹(0.5)
- tan⁻¹(2)
- tan⁻¹(1)
- 30°
Difficulty: Medium · Topic: Relative Velocity
Solution
tanθ = v_man/v_rain = 5/10 = 0.5. θ = tan⁻¹(0.5) ≈ 26.57°.
Q12. A projectile is fired at 30° with velocity 20 m/s. Maximum height is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 20²×sin²30°/20 = 5.0 m.
Q13. A projectile is fired at 30° with velocity 20 m/s. The range is (g=10 m/s²):
- 39.64 m
- 34.64 m
- 69.28 m
- 17.32 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 20²×sin60°/10 = 34.64 m.
Q14. A projectile is fired at 45° with velocity 20 m/s. Maximum height is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 20²×sin²45°/20 = 10.0 m.
Q15. A projectile is fired at 45° with velocity 20 m/s. The range is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 20²×sin90°/10 = 40.0 m.
Q16. A projectile is fired at 60° with velocity 20 m/s. Maximum height is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 20²×sin²60°/20 = 15.0 m.
Q17. A projectile is fired at 60° with velocity 20 m/s. The range is (g=10 m/s²):
- 34.64 m
- 39.64 m
- 17.32 m
- 69.28 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 20²×sin120°/10 = 34.64 m.
Q18. A projectile is fired at 30° with velocity 30 m/s. Maximum height is (g=10 m/s²):
- 11.25 m
- 22.5 m
- 5.62 m
- 14.25 m
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 30²×sin²30°/20 = 11.25 m.
Q19. A projectile is fired at 30° with velocity 30 m/s. The range is (g=10 m/s²):
- 38.97 m
- 82.94 m
- 155.88 m
- 77.94 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 30²×sin60°/10 = 77.94 m.
Q20. A projectile is fired at 45° with velocity 30 m/s. Maximum height is (g=10 m/s²):
- 25.5 m
- 45.0 m
- 11.25 m
- 22.5 m
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 30²×sin²45°/20 = 22.5 m.
Q21. A projectile is fired at 45° with velocity 30 m/s. The range is (g=10 m/s²):
- 90.0 m
- 180.0 m
- 45.0 m
- 95.0 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 30²×sin90°/10 = 90.0 m.
Q22. A projectile is fired at 30° with velocity 40 m/s. Maximum height is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 40²×sin²30°/20 = 20.0 m.
Q23. A projectile is fired at 30° with velocity 40 m/s. The range is (g=10 m/s²):
- 138.56 m
- 143.56 m
- 69.28 m
- 277.12 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 40²×sin60°/10 = 138.56 m.
Q24. A projectile is fired at 60° with velocity 40 m/s. Maximum height is (g=10 m/s²):
- 63.0 m
- 120.0 m
- 60.0 m
- 30.0 m
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 40²×sin²60°/20 = 60.0 m.
Q25. A projectile is fired at 60° with velocity 40 m/s. The range is (g=10 m/s²):
- 277.12 m
- 69.28 m
- 143.56 m
- 138.56 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 40²×sin120°/10 = 138.56 m.
Q26. A projectile is fired at 45° with velocity 50 m/s. Maximum height is (g=10 m/s²):
- 62.5 m
- 31.25 m
- 65.5 m
- 125.0 m
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 50²×sin²45°/20 = 62.5 m.
Q27. A projectile is fired at 45° with velocity 50 m/s. The range is (g=10 m/s²):
- 500.0 m
- 125.0 m
- 250.0 m
- 255.0 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 50²×sin90°/10 = 250.0 m.
Q28. A projectile is fired at 45° with velocity 10 m/s. Maximum height is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 10²×sin²45°/20 = 2.5 m.
Q29. A projectile is fired at 45° with velocity 10 m/s. The range is (g=10 m/s²):
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 10²×sin90°/10 = 10.0 m.
Q30. A projectile is fired at 30° with velocity 25 m/s. Maximum height is (g=10 m/s²):
- 7.81 m
- 15.62 m
- 10.81 m
- 3.9 m
Difficulty: Medium · Topic: Projectile Motion
Solution
H = u²sin²θ/(2g) = 25²×sin²30°/20 = 7.81 m.
Q31. A projectile is fired at 30° with velocity 25 m/s. The range is (g=10 m/s²):
- 54.13 m
- 108.26 m
- 59.13 m
- 27.07 m
Difficulty: Medium · Topic: Projectile Range
Solution
R = u²sin2θ/g = 25²×sin60°/10 = 54.13 m.
Q32. A projectile is launched at 30° with speed 20 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 2.0 s.
Q33. A projectile is launched at 35° with speed 25 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 2.87 s.
Q34. A projectile is launched at 40° with speed 30 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 3.86 s.
Q35. A projectile is launched at 45° with speed 35 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 4.95 s.
Q36. A projectile is launched at 50° with speed 40 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 6.13 s.
Q37. A projectile is launched at 55° with speed 45 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 7.37 s.
Q38. A projectile is launched at 60° with speed 50 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 8.66 s.
Q39. A projectile is launched at 65° with speed 55 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 9.97 s.
Q40. A projectile is launched at 70° with speed 60 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 11.28 s.
Q41. A projectile is launched at 75° with speed 65 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 12.56 s.
Q42. A projectile is launched at 80° with speed 70 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 13.79 s.
Q43. A projectile is launched at 85° with speed 75 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 14.94 s.
Q44. A projectile is launched at 90° with speed 80 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 16.0 s.
Q45. A projectile is launched at 95° with speed 85 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 16.94 s.
Q46. A projectile is launched at 100° with speed 90 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 17.73 s.
Q47. A projectile is launched at 105° with speed 95 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 18.35 s.
Q48. A projectile is launched at 110° with speed 100 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 18.79 s.
Q49. A projectile is launched at 115° with speed 105 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 19.03 s.
Q50. A projectile is launched at 120° with speed 110 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 19.05 s.
Q51. A projectile is launched at 125° with speed 115 m/s. Time of flight is (g=10):
Difficulty: Medium · Topic: Projectile
Solution
T = 2usinθ/g = 18.84 s.
Q52. Projectile: u=10m/s, θ=15°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=0.33 m.
Q53. Projectile: u=10m/s, θ=15°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=5.0 m.
Q54. Projectile: u=10m/s, θ=15°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=0.52 s.
Q55. Projectile: u=10m/s, θ=30°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=1.25 m.
Q56. Projectile: u=10m/s, θ=30°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=8.66 m.
Q57. Projectile: u=10m/s, θ=30°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.0 s.
Q58. Projectile: u=10m/s, θ=37°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=1.81 m.
Q59. Projectile: u=10m/s, θ=37°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=9.61 m.
Q60. Projectile: u=10m/s, θ=37°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.2 s.
Q61. Projectile: u=10m/s, θ=45°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=2.5 m.
Q62. Projectile: u=10m/s, θ=45°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=10.0 m.
Q63. Projectile: u=10m/s, θ=45°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.41 s.
Q64. Projectile: u=10m/s, θ=53°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=3.19 m.
Q65. Projectile: u=10m/s, θ=53°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=9.61 m.
Q66. Projectile: u=10m/s, θ=53°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.6 s.
Q67. Projectile: u=10m/s, θ=60°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=3.75 m.
Q68. Projectile: u=10m/s, θ=60°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=8.66 m.
Q69. Projectile: u=10m/s, θ=60°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.73 s.
Q70. Projectile: u=10m/s, θ=75°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=4.67 m.
Q71. Projectile: u=10m/s, θ=75°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=5.0 m.
Q72. Projectile: u=10m/s, θ=75°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.93 s.
Q73. Projectile: u=15m/s, θ=15°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=0.75 m.
Q74. Projectile: u=15m/s, θ=15°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=11.25 m.
Q75. Projectile: u=15m/s, θ=15°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=0.78 s.
Q76. Projectile: u=15m/s, θ=30°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=2.81 m.
Q77. Projectile: u=15m/s, θ=30°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=19.49 m.
Q78. Projectile: u=15m/s, θ=30°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.5 s.
Q79. Projectile: u=15m/s, θ=37°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=4.07 m.
Q80. Projectile: u=15m/s, θ=37°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=21.63 m.
Q81. Projectile: u=15m/s, θ=37°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.81 s.
Q82. Projectile: u=15m/s, θ=45°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=5.62 m.
Q83. Projectile: u=15m/s, θ=45°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=22.5 m.
Q84. Projectile: u=15m/s, θ=45°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.12 s.
Q85. Projectile: u=15m/s, θ=53°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=7.18 m.
Q86. Projectile: u=15m/s, θ=53°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=21.63 m.
Q87. Projectile: u=15m/s, θ=53°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.4 s.
Q88. Projectile: u=15m/s, θ=60°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=8.44 m.
Q89. Projectile: u=15m/s, θ=60°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=19.49 m.
Q90. Projectile: u=15m/s, θ=60°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.6 s.
Q91. Projectile: u=15m/s, θ=75°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=10.5 m.
Q92. Projectile: u=15m/s, θ=75°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=11.25 m.
Q93. Projectile: u=15m/s, θ=75°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.9 s.
Q94. Projectile: u=20m/s, θ=15°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=1.34 m.
Q95. Projectile: u=20m/s, θ=15°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=20.0 m.
Q96. Projectile: u=20m/s, θ=15°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=1.04 s.
Q97. Projectile: u=20m/s, θ=30°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=5.0 m.
Q98. Projectile: u=20m/s, θ=30°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=34.64 m.
Q99. Projectile: u=20m/s, θ=30°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.0 s.
Q100. Projectile: u=20m/s, θ=37°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=7.24 m.
Q101. Projectile: u=20m/s, θ=37°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=38.45 m.
Q102. Projectile: u=20m/s, θ=37°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.41 s.
Q103. Projectile: u=20m/s, θ=45°. Max height (g=10):
Difficulty: Medium · Topic: Projectile
Solution
H=u²sin²θ/2g=10.0 m.
Q104. Projectile: u=20m/s, θ=45°. Range (g=10):
Difficulty: Medium · Topic: Range
Solution
R=u²sin2θ/g=40.0 m.
Q105. Projectile: u=20m/s, θ=45°. Time of flight (g=10):
Difficulty: Medium · Topic: Time of Flight
Solution
T=2usinθ/g=2.83 s.
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