# A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr, at an angle $\theta$ with respect to the river. If AB=BC=400m. Then- (1) time taken by the man is 12 min (2) time taken by the man is 8 min (3) the value of $\theta$ is 45$°$ (4) the value of $\theta$ is 53$°$

Subtopic:  Relative Motion |
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A body is thrown horizontally with a velocity $\sqrt{2gh}$ from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is:

1. h

2. $\frac{h}{2}$

3. 2h

4. $\frac{2h}{3}$

Subtopic:  Projectile Motion |
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Two men P & Q are standing at corners A & B of square ABCD of side 8 m. They start moving along the track with constant speed 2 m/s and 10 m/s respectively. The time when they will meet for the first time, is equal to:

1. 2 sec

2. 3 sec

3. 1 sec

4. 6 sec

Subtopic:  Relative Motion |
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A particle starts from the origin at t=0 and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is $y=b{x}^{2}$. The x component of its velocity (at t=0) is:

(1) variable

(2) $\sqrt{\frac{2a}{b}}$

(3) $\frac{a}{2b}$

(4) $\sqrt{\frac{a}{2b}}$

Subtopic:  Acceleration |
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A body is projected with a velocity u with an angle of projection $\theta$. Change in velocity after the time (t) from the time of projection will be

1. gt

2. $\frac{1}{2}g{t}^{2}$

3. u sin$\theta$

4. u cos$\theta$

Subtopic:  Projectile Motion |
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What determines the nature of the path followed by the particle?

(1) Speed only

(2) Velocity only

(3) Acceleration only

(4) None of these

Subtopic:  Projectile Motion |
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A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is :

(1) 10 km/hr

(2) 8 km/hr

(3) 6 km/hr

(4) 4 km/hr

Subtopic:  Relative Motion |
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A boat is moving with velocity of $3\stackrel{^}{i}+4\stackrel{^}{j}$ in river and water is moving with a velocity of $-3\stackrel{^}{i}-4\stackrel{^}{j}$ with respect to ground. Relative velocity of boat with respect to water is:

(1) $-6\stackrel{^}{i}-8\stackrel{^}{j}$

(2) $6\stackrel{^}{i}+8\stackrel{^}{j}$

(3) $8\stackrel{^}{j}$

(4) $6\stackrel{^}{i}$

Subtopic:  Relative Motion |
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A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip(returning to the initial point) is:

(1) 5 min

(2) 60 min

(3) 20 min

(4) 30 min

Subtopic:  Relative Motion |
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A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south.

(1) 30° with downstream

(2) 60° with downstream

(3) 120° with downstream

(4) South

Subtopic:  Relative Motion |
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