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In a projectile motion the velocity,
| 1. | is always perpendicular to the acceleration |
| 2. | is never perpendicular to the acceleration |
| 3. | is perpendicular to the acceleration for one instant only |
| 4. | is perpendicular to the acceleration for two instants |
Subtopic: Â Projectile Motion |
 65%
Level 2: 60%+
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A projectile is fired so as to give a maximum horizontal range of \(1\) km. What would be the maximum height reached by it if it were to be fired vertically upward?
| 1. | \(2\) km | 2. | \(1\) km |
| 3. | \(\dfrac12\) km | 4. | \(\dfrac14\) km |
Subtopic: Â Projectile Motion |
 56%
Level 3: 35%-60%
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Consider the two situations shown in the figures. In figure (A), the particle \(P\) is given a velocity \(u\) up a smooth horizontal incline and it reaches a maximum vertical height \(h_A\). In figure (B), the same particle \(P\) is projected with a velocity \(u\) at an angle \(\theta\) (parallel to the previous incline) and reaches a maximum height \(h_B\).Then,
| 1. | \(h_A=h_B~\text{sin}\theta\) | 2. | \(h_A~\text{sin}\theta=h_B\) |
| 3. | \(h_A~\text{sin}^2\theta=h_B\) | 4. | \(\dfrac{h_A}{\text{sin}^2\theta}=h_B\) |
Subtopic: Â Projectile Motion |
 53%
Level 3: 35%-60%
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Two projectiles are launched, one at twice the speed of the other; the slower one at \(30^\circ\) and the faster one at \(60^\circ.\) Their horizontal ranges are in the ratio: (slower : faster)
| 1. | \(\dfrac{1}{2}\) | 2. | \(\dfrac{1}{4}\) |
| 3. | \(\dfrac{1}{6}\) | 4. | \(\dfrac{1}{12}\) |
Subtopic: Â Projectile Motion |
 77%
Level 2: 60%+
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The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
| 1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |
| 3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |
Subtopic: Â Projectile Motion |
 84%
Level 1: 80%+
AIPMT - 2013
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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:
1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)
2. \(\theta = \tan^{-1}(4)\)
3. \(\theta = \tan^{-1}(2)\)
4. \(\theta = 45^{\circ}\)
1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)
2. \(\theta = \tan^{-1}(4)\)
3. \(\theta = \tan^{-1}(2)\)
4. \(\theta = 45^{\circ}\)
Subtopic: Â Projectile Motion |
 78%
Level 2: 60%+
AIPMT - 2012
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If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) and \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?
| 1. | time of flight |
| 2. | horizontal range of projectile |
| 3. | maximum height acquired |
| 4. | all of the above |
Subtopic: Â Projectile Motion |
 81%
Level 1: 80%+
AIPMT - 2000
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