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Q. No.

The equation of the trajectory of a projectile is given as \(y = 4x-\dfrac{1}{4x^2}.\) The range of the projectile is:

1. 1 m

2. 32 m

3. 16 m

4. 48 m

Subtopic:  Projectile Motion |
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Two projectiles are thrown at an angle of projection \(\alpha\) and \(\beta\) with the horizontal. If \(\alpha+\beta=90^\circ,\) then the ratio of the range of two projectiles on the horizontal plane is equal to:
1. \(1:1\)
2. \(2:1\)
3. \(1:2\)
4. \(1:3\)
Subtopic:  Projectile Motion |
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A projectile is fired from the surface of the earth with a velocity of \(5\text{ m/s}\) and at an angle \(\theta \) with the horizontal. Another projectile fired from another planet with a velocity of \(3\text{ m/s}\) at the same angle follows a trajectory that is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is: (given = \(9.8\text{ m/s}^2\))

1. \(3.5\)

2. \(5.9\)

3. \(16.3\)

4. \(110.8\)

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Two particles \(A\) and \(B\) are projected with speeds \(40\text{ m/s}\) and \(60\text{ m/s}\) at angles \(30^{\circ}\) and \(60^{\circ}\) above the horizontal, respectively. What is the ratio of the range of \(A\) to the range of \(B\text{?}\)
1. \(\sqrt 2 : 3\)
2. \(\sqrt 3: 2\)
3. \(4:9\)
4. \(2:1\)
Subtopic:  Projectile Motion |
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Two projectiles are fired from the same point with the same speed at angles of projection \(60^\circ\) and \(30^\circ\) respectively. Which one of the following is true?
1. Their time of flight will be the same.
2. Their maximum height will be the same.
3. Their range will be the same.
4. Their landing velocity will be the same.
Subtopic:  Projectile Motion |
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The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

1. \(90^{\circ}\)

2. \(60^{\circ}\)

3. \(45^{\circ}\)

4. \(30^{\circ}\)

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Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first?

1. slower one
2. faster one
3. both will reach simultaneously
4. cannot be predicted
Subtopic:  Projectile Motion |
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An arrow is shot into the air with a range of \(200\) m and a flight time of \(5\) s. Assuming \(g\) to be \(10~\text{m/s}^2,\) what is the horizontal component of the arrow's velocity?
1. \(25~\text{m/s} \) 2. \(40~\text{m/s}\)
3. \(31.25~\text{m/s}\) 4. \(12.5~\text{m/s}\)
Subtopic:  Projectile Motion |
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Given below are two statements: 
Assertion (A): When a body is projected at an angle of \(45^\circ,\) its range is maximum.
Reason (R): For maximum range, the value of \(\text{sin}2 \theta\) should be equal to one.
  
1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. Both (A) and (R) are false.
Subtopic:  Projectile Motion |
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A boy throws two balls \(A, B\) from the window of a tall multi-storeyed building. Ball \(A\) is dropped from rest, while ball \(B\) is given an initial horizontal speed of \(30~\text{m/s}.\) The position of the boy is at a level of \(80~\text m\) above the ground, and the balls are thrown simultaneously. Ignore air resistance, and take \(g=10~\text{m/s}^2.\)
Ball \(A\) reaches the ground in:
1. \(8~\text s\)
2. \(4~\text s\)
3. \(2~\text s\)
4. \(\sqrt8~\text s\)
Subtopic:  Projectile Motion |
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