If a body is projected from the surface of the earth for maximum range R, then the maximum height attained by the body is:

(1) R

(2) R8

(3) 4R

(4) R4

Subtopic:  Projectile Motion |
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Level 1: 80%+
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A projectile is projected from the ground with the velocity \(v_{0}\) at an angle \(\theta\) with the horizontal. What is the vertical component of the velocity of the projectile when its vertical displacement is equal to half of the maximum height attained?
1. \(\sqrt{3} v_{0}\cos\theta\)
2. \(\frac{v_{0}}{\sqrt{2}} \sin\theta\)
3. \(\frac{v_{0}}{\sqrt{2}} \cos \theta\)

4. \(\sqrt{5} v_{0}\)

Subtopic:  Projectile Motion |
 72%
Level 2: 60%+
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A projectile is projected with a speed of 60 m/s at an angle of 60° from the horizontal. After some time projectile is moving at an angle of 30° with horizontal, what is the value of ddtv at this instant? (Given g = 10 m/s2)

(1) 1 m/s2

(2) 53 m/s2

(3) 53 m/s2

(4) 5 m/s2

Subtopic:  Projectile Motion |
Level 3: 35%-60%
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A particle is rotating with increasing speed on a circular track. The angle between its radius vector and acceleration is θ, then:

(1) 0° < θ < 90°

(2) 45° < θ < 90°

(3) 90° < θ < 180°

(4) θ = 90°

Subtopic:  Circular Motion |
Level 3: 35%-60%
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A particle starts moving on a circular path from rest, such that its tangential acceleration varies with time as \(a_t=kt\). Distance traveled by particle on the circular path in time \(t\) is:
1. \( \frac{kt^3}{3} \)
2. \(\frac{kt^2}{6} \)
3. \(\frac{kt^3}{6} \)
4. \(\frac{k t^2}{2}\)

Subtopic:  Circular Motion |
 72%
Level 2: 60%+
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A projectile thrown from the ground has horizontal range R. If velocity at the highest point is doubled somehow, the new range will be:

(1) 3 R

(2) 1.5 R

(3) 3 R

(4) 2 R

Subtopic:  Projectile Motion |
Level 3: 35%-60%
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The time of flights for a particle thrown for equal range at different angles is 4 sec and 3 sec. Speed of projection is:

(1) 10 m/s

(2) 20 m/s

(3) 25 m/s

(4) 50 m/s

Subtopic:  Projectile Motion |
 68%
Level 2: 60%+
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A body is projected from the ground at a speed v at an angle θ above the horizontal. The radius of curvature of its path at the highest point is:

(1)  v2cos2θ2g

(2)  vcosθg

(3)  vcos2θg

(4)  v2cos2θg

Subtopic:  Projectile Motion |
 53%
Level 3: 35%-60%
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A particle is projected from the origin with velocity 4i^+9j^ m/s. The acceleration in the region is constant and -10j^ m/s2. The magnitude of velocity after one second is

(1) 8 m/s

(2) 15 m/s

(3) 17 m/s

(4) 27 m/s

Subtopic:  Projectile Motion |
 83%
Level 1: 80%+
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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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