A projectile is given an initial velocity of $\stackrel{^}{i}+2\stackrel{^}{j}$. The cartesian equation of its path is (g = 10 ${\mathrm{ms}}^{-2}$)  1. $\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^{2}$ 2. $\mathrm{y}=\mathrm{x}-5{\mathrm{x}}^{2}$ 3. $4\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^{2}$ 4. $\mathrm{y}=2\mathrm{x}-25{\mathrm{x}}^{2}$

Subtopic:  Projectile Motion |
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A ship A is moving westwards with a speed of 10 km ${\mathrm{h}}^{-1}$ and a ship B, 100 km south of A is moving northwards with a speed of 10 km ${\mathrm{h}}^{-1}$. The time after which the distance between them becomes the shortest, is:

1. 5 hr

2. $5\sqrt{2}$ hr

3. $10\sqrt{2}$ hr

4. 0 hr

Subtopic:  Relative Motion |
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Time taken by the projectile to reach from A to B is t. Then the distance AB is equal to :

1. $\frac{ut}{\sqrt{3}}$

2. $\frac{\sqrt{3}ut}{2}$

3. $\sqrt{3}ut$

4. 2ut

Subtopic:  Projectile Motion |
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A particle projected with kinetic energy ${\mathrm{k}}_{0}$ with an angle of projection $\mathrm{\theta }$. Then the variation of kinetic K with vertical displacement y is

1.  linear

2.  parabolic

3.  hyperbolic

4.  periodic

Subtopic:  Projectile Motion |
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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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