A ship A is moving Westwards with a speed of 10 kmph and a ship B 100 km South of A, is moving Northwards with a speed of 10 kmph. The time after which the distance between them becomes the shortest is:
1. 0 h
2. 5 h
3. $5\sqrt{2}$h
4. $10\sqrt{2}$h

Subtopic:  Relative Motion |
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Two particles A and B, move with constant velocities $$\overrightarrow{\mathrm{v}_1}$$ and $$\overrightarrow{\mathrm{v}_2}$$ respectively. At the initial moment, their position vectors are $$\overrightarrow{\mathrm{r}_1}$$ and $$\overrightarrow{\mathrm{r}_2}$$ respectively. The condition for particles A and B for their collision will be:

1.$$\frac{\overrightarrow{r_1}-\overrightarrow{r_2}}{\left|\overrightarrow{r_1}-\overrightarrow{r_2}\right|}=\frac{\overrightarrow{v_2}-\overrightarrow{v_1}}{\left|\overrightarrow{v_2}-\overrightarrow{v_1}\right|}$$
2. $$\overrightarrow{r_1} \cdot \overrightarrow{v_1}=\overrightarrow{r_2} \cdot \overrightarrow{v_2}$$   ${\mathrm{}}_{}$

3. $$\overrightarrow{r_1} \times \overrightarrow{v_1}=\overrightarrow{r_2} \times \overrightarrow{v_2}$$

4. $$\overrightarrow{r_1}-\overrightarrow{r_2}=\overrightarrow{v_1}-\overrightarrow{v_2}$$

Subtopic:  Relative Motion |
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The position vector of a particle R as a function of time t is given by
$\stackrel{\to }{\mathrm{R}}=4\mathrm{sin}\left[2\mathrm{\pi t}\right]\stackrel{^}{\mathrm{i}}+4\mathrm{cos}\left[2\mathrm{\pi t}\right]\stackrel{^}{\mathrm{j}}$
Where R is in meters, t is in seconds and $\stackrel{^}{\mathrm{i}},$ $\stackrel{^}{\mathrm{j}}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

 1 Acceleration is along -$$\overrightarrow{R}$$ . 2 Magnitude of the acceleration vector is $$\frac{V^2}{R}$$, where v is the velocity of the particle. 3 Magnitude of the velocity of the particle is 8 m/s. 4 Path of the particle is a circle of radius 4m.
Subtopic:  Circular Motion |
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A projectile is fired from the surface of the earth with a velocity of 5ms–1 and at an angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3ms–1 at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is: (given g = 9.8 ms–2)

1. 3.5 m/s2

2. 5.9 m/s2

3. 16.3 m/s2

4. 110.8 m/s2

Subtopic:  Projectile Motion |
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The velocity of a projectile at the initial point $$A$$ is $$2\hat i+3\hat j~$$m/s. Its velocity (in m/s) at 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. $\theta ={\mathrm{tan}}^{-1}\left(\frac{1}{4}\right)$
2. $\theta ={\mathrm{tan}}^{-1}\left(4\right)$
3. $\theta ={\mathrm{tan}}^{-1}\left(2\right)$
4. $\theta ={45}^{0}$

Subtopic:  Projectile Motion |
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A particle moves in a circle of radius $$5$$ cm with constant speed and time period $$0.2\pi$$ s. The acceleration of the particle is:
1. $$25$$ m/s2
2. $$36$$ m/s2
3. $$5$$ m/s2
4. $$15$$ m/s2

Subtopic:  Circular Motion |
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A body is moving with a velocity of $$30$$ m/s towards the east. After $$10$$ s, its velocity becomes $$40$$ m/s towards the north. The average acceleration of the body is:
1. $$7 \mathrm{~m} / \mathrm{s}^2$$
2. $$\sqrt{7} \mathrm{~m} / \mathrm{s}^2$$
3. $$5 \mathrm{~m} / \mathrm{s}^2$$
4. $$1 \mathrm{~m} / \mathrm{s}^2$$

Subtopic:  Acceleration |
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A missile is fired for a maximum range with an initial velocity of 20 m/s. If g= 10 m/s2, then the range of the missile will be:

1.  50 m

2.  60 m

3.  20 m

4.  40 m

Subtopic:  Projectile Motion |
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A projectile is fired at an angle of $$45^\circ$$ with the horizontal. The elevation angle $$\alpha$$ of the projectile at its highest point, as seen from the point of projection is:
1. $$60^\circ$$
2. $$tan^{-1}\left ( \frac{1}{2} \right )$$
3. $$tan^{-1}\left ( \frac{\sqrt{3}}{2} \right )$$
4. $$45^\circ$$

Subtopic:  Projectile Motion |
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