physics : class11 Horizontal Range : Projectile Motion : Kinematics MCQ Questions and Answers
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Horizontal Range
MCQ questions and answers.
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MCQ Questions
1. For a projectile launched and landing at the same level with speed u and angle θ, what is its horizontal range?
A.
u sinθ/g
B.
u² sin2θ/g
C.
u² cosθ/g
D.
2u sinθ/g
Correct Answer:
u² sin2θ/g
Explanation:
For a projectile returning to its launch level, the horizontal range is R = u² sin2θ/g.
2. At what angle of projection is the horizontal range maximum for a projectile landing at the same level?
A.
30°
B.
45°
C.
60°
D.
90°
Correct Answer:
45°
Explanation:
The range is R = u² sin2θ/g. It is maximum when sin2θ = 1, which occurs at 2θ = 90°, so θ = 45°.
3. Two projectiles are launched with the same speed at angles 30° and 60° above the horizontal. How do their horizontal ranges compare when they land at the same level?
A.
The range at 30° is greater
B.
The range at 60° is greater
C.
Both ranges are equal
D.
Both ranges are zero
Correct Answer:
Both ranges are equal
Explanation:
Complementary angles have equal ranges because sin(2 × 30°) = sin(2 × 60°) = sin60°.
4. If the initial speed of a projectile is doubled while its angle of projection remains unchanged, how does its horizontal range change?
A.
It becomes half
B.
It remains unchanged
C.
It becomes twice
D.
It becomes four times
Correct Answer:
It becomes four times
Explanation:
Since R = u² sin2θ/g, the range is proportional to the square of the initial speed. Doubling u makes the range four times.
5. A projectile is launched with speed 20 m/s at 45° to the horizontal. Taking g = 10 m/s², what is its horizontal range?
A.
20 m
B.
30 m
C.
40 m
D.
50 m
Correct Answer:
40 m
Explanation:
R = u² sin90°/g = 20² × 1/10 = 40 m.
6. For a fixed initial speed, which factor determines the horizontal range of a projectile launched and landing at the same level?
A.
The angle of projection
B.
The colour of the projectile
C.
The mass of the projectile only
D.
The shape of the launch platform
Correct Answer:
The angle of projection
Explanation:
For fixed speed and gravitational acceleration, R = u² sin2θ/g, so the range depends on the angle of projection.
7. A projectile has a horizontal range of 80 m when launched at 45°. What will be its range if it is launched with the same speed at 30°, assuming it lands at the same level?
A.
40 m
B.
60 m
C.
69.3 m
D.
80 m
Correct Answer:
69.3 m
Explanation:
At 45°, the range is u²/g = 80 m. At 30°, the range is (u²/g)sin60° = 80 × 0.866 ≈ 69.3 m.
8. A projectile is launched at 20° and another at 70° with the same speed. If both land at the same level, how do their horizontal ranges compare?
A.
The 20° projectile has twice the range
B.
The 70° projectile has twice the range
C.
Their ranges are equal
D.
Their ranges cannot be compared
Correct Answer:
Their ranges are equal
Explanation:
The angles 20° and 70° are complementary. Therefore, sin40° = sin140°, giving equal horizontal ranges.
9. What is the maximum horizontal range of a projectile launched with speed 10 m/s, taking g = 10 m/s²?
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Correct Answer:
10 m
Explanation:
Maximum range occurs at 45°. Thus Rmax = u²/g = 10²/10 = 10 m.
10. If the angle of projection is changed from 45° to 90° while the initial speed remains constant, what happens to the horizontal range?
A.
It becomes maximum
B.
It becomes half
C.
It becomes zero
D.
It becomes twice
Correct Answer:
It becomes zero
Explanation:
For 90°, R = u² sin180°/g = 0, because the projectile has no horizontal component of velocity.