The speed of a boat in still water is half of the velocity of the flow of water(v). At what angle boat should steer with the direction of flow of water so that drift of boat is minimum?

(1) 30°

(2) 60°

(3) 90°

(4) 120°

Subtopic:  Relative Motion |
 56%
Level 3: 35%-60%
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A sports car travels at \(20~\text{m/s}\) along a horizontal road. A camera positioned \(40~\text{m}\) horizontally away from the road (as shown in the diagram) tracks the car at a \(45^\circ\) viewing angle. What angular velocity must the camera rotate at to keep the car in focus?

           

1. \(1.000~\text{rad/s}\)
2. \(0.500~\text{rad/s}\)
3. \(0.250~\text{rad/s}\)
4. \(0.125~\text{rad/s}\)

Subtopic:  Circular Motion |
Level 3: 35%-60%
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The magnitude of a vector A is constant but it is changing its direction continuously. The angle between A and dAdt is :

(1) 180°

(2) 120°

(3) 90°

(4) 0°

Subtopic:  Circular Motion |
 71%
Level 2: 60%+
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A particle is moving on a circular path of radius \(R.\) When the particle moves from point \(A\) to \(B\) (angle \( \theta\)), the ratio of the distance to that of the magnitude of the displacement will be:

         
1. \(\dfrac{\theta}{\sin\frac{\theta}{2}}\)
2. \(\dfrac{\theta}{2\sin\frac{\theta}{2}}\)
3. \(\dfrac{\theta}{2\cos\frac{\theta}{2}}\)
4. \(\dfrac{\theta}{\cos\frac{\theta}{2}}\)

Subtopic:  Position & Displacement |
 76%
Level 2: 60%+
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Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and the diameter \(AB.\) If the time taken by both particles is the same, then the ratio of magnitudes of their average velocities is:
                                
1. \(2\)
2. \(2\sqrt{3}\)

3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)

Subtopic:  Speed & Velocity |
 63%
Level 2: 60%+
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A particle moves on the curve \(x^2 = 2y\). The angle of its velocity vector with the \(x\)-axis at the point \(\left(1, \frac{1}{2}\right )\) will be:

1. \(30^\circ\) 2. \(60^\circ\)
3. \(45^\circ\) 4. \(75^\circ\)
Subtopic:  Speed & Velocity |
 63%
Level 2: 60%+
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A ball is projected at an angle θ with the horizontal. The angle of elevation of the ball when it is at the highest point is:

(1)  tanθ2

(2)  sinθ2

(3)  cosθ2

(4)  2tanθ

Subtopic:  Projectile Motion |
 68%
Level 2: 60%+
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A particle is moving along a curve. Select the correct statement.

1. If its speed is constant, then it has no acceleration.
2. If its speed is increasing, then the acceleration of the particle is along its direction of motion.
3. If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion.
4. If its speed is constant, its acceleration is perpendicular to its velocity.
Subtopic:  Acceleration |
 71%
Level 2: 60%+
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A man can row a boat with \(8\) km/h in still water. He is crossing a river of width \(8\) km, where the speed of water flow is \(4\) km/h. What direction should he head the boat to cross the river in the shortest time?
1. \(30^{\circ}\) with the current
2. \(60^{\circ}\) with the current
3. \(90^{\circ}\) with the current
4. \(120^{\circ}\) with the current

Subtopic:  Relative Motion |
 59%
Level 3: 35%-60%
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The horizontal range of a particle thrown from the ground is four times the maximum height. The angle of projection with the vertical is:

(1) 60°

(2) 30°

(3) 45°

(4) 90°

Subtopic:  Projectile Motion |
 88%
Level 1: 80%+
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