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:  Projectile Motion |
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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:  Projectile Motion |
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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. \(\frac{h_A}{\text{sin}^2\theta}=h_B\)
Subtopic:  Projectile Motion |
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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:  Projectile Motion |
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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:  Projectile Motion |
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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. \(\theta = 45^{\circ}\)
Subtopic:  Projectile Motion |
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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:  Projectile Motion |
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