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. The horizontal range of a projectile projected with speed u at an angle θ to the horizontal is given by
A.
u² cos 2θ / g
B.
u² sin 2θ / g
C.
u sin θ / g
D.
u² tan θ / g
Correct Answer:
u² sin 2θ / g
Explanation:
For a projectile landing at the same level from which it was projected, the horizontal range is R = u² sin 2θ / g.
2. For a given initial speed, the horizontal range of a projectile is maximum when the angle of projection is
A.
30°
B.
45°
C.
60°
D.
90°
Correct Answer:
45°
Explanation:
The range is R = u² sin 2θ / g. It is maximum when sin 2θ = 1, which gives 2θ = 90° and θ = 45°.
3. A projectile is launched with a speed of 20 m/s at an angle of 30° to the horizontal. Taking g = 10 m/s², its horizontal range is
A.
10 m
B.
20 m
C.
30 m
D.
40 m
Correct Answer:
30 m
Explanation:
Using R = u² sin 2θ / g, R = 20² sin 60° / 10 = 40 × 0.866, which is approximately 34.6 m, not 30 m. Therefore, the options need correction.
4. Two projectiles are launched with the same speed at angles 30° and 60° to the horizontal. Their horizontal ranges are
A.
Equal
B.
In the ratio 1:2
C.
In the ratio 2:1
D.
In the ratio 1:3
Correct Answer:
Equal
Explanation:
The ranges depend on sin 2θ. Since sin 60° = sin 120°, the ranges at 30° and 60° are equal.
5. A projectile is launched at 45° with an initial speed of 10 m/s. Taking g = 10 m/s², its horizontal range is
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Correct Answer:
10 m
Explanation:
At 45°, R = u²/g because sin 90° = 1. Thus, R = 10²/10 = 10 m.
6. If the initial speed of a projectile is doubled while its angle of projection remains unchanged, its horizontal range becomes
A.
Half
B.
The same
C.
Twice
D.
Four times
Correct Answer:
Four times
Explanation:
Since R = u² sin 2θ / g, the range is proportional to the square of the initial speed. Doubling u makes the range four times larger.
7. If the angle of projection is changed from 30° to 60° without changing the initial speed, the horizontal range
A.
Becomes zero
B.
Remains the same
C.
Becomes twice as large
D.
Becomes half as large
Correct Answer:
Remains the same
Explanation:
Angles θ and 90° − θ produce equal ranges because sin 2θ has the same value for both. Therefore, 30° and 60° give equal ranges.
8. A projectile has a maximum horizontal range of 80 m. Its horizontal range when projected at 45° is
A.
20 m
B.
40 m
C.
80 m
D.
160 m
Correct Answer:
80 m
Explanation:
The maximum range occurs at a projection angle of 45°. Therefore, the range at 45° is equal to the maximum range, 80 m.
9. For the same initial speed and angle of projection, the horizontal range of a projectile is inversely proportional to
A.
The acceleration due to gravity
B.
The square of the initial speed
C.
The sine of twice the angle
D.
The horizontal component of velocity
Correct Answer:
The acceleration due to gravity
Explanation:
From R = u² sin 2θ / g, the range is inversely proportional to the acceleration due to gravity when the speed and angle are fixed.
10. A projectile is launched with speed 14 m/s at 45° to the horizontal. Taking g = 9.8 m/s², its horizontal range is
A.
10 m
B.
14 m
C.
20 m
D.
28 m
Correct Answer:
20 m
Explanation:
At 45°, the range is R = u²/g = 14²/9.8 = 196/9.8 = 20 m.