A ship $$A$$ is moving westward with a speed of $$10$$ kmph and a ship $$B$$, $$100 ~\text{km}$$ South of $$A$$, is moving northward with a speed of $$10$$ $$\text{kmph}$$. 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 |
From NCERT
NEET - 2015
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Two particles $$\mathrm{A}$$ and $$\mathrm{B}$$, move with constant velocities $$\overrightarrow{{v}_1}$$ and $$\overrightarrow{{v}_2}$$ respectively. At the initial moment, their position vectors are $$\overrightarrow{{r}_1}$$ and $$\overrightarrow{{r}_2}$$ respectively. The condition for particles $$\mathrm{A}$$ and $$\mathrm{B}$$ for their collision will be:
1.$$\dfrac{\vec{r_1}-\vec{r_2}}{\left|\vec{r_1}-\vec{r_2}\right|}=\dfrac{\vec{v_2}-\vec{v_1}}{\left|\vec{v_2}-\vec{v_1}\right|}$$
2. $$\vec{r_1} \cdot \vec{v_1}=\vec{r_2} \cdot \vec{v_2}$$   ${\mathrm{}}_{}$
3. $$\vec{r_1} \times \vec{v_1}=\vec{r_2} \times \vec{v_2}$$
4. $$\vec{r_1}-\vec{r_2}=\vec{v_1}-\vec{v_2}$$

Subtopic:  Relative Motion |
69%
From NCERT
NEET - 2015
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The position vector of a particle $$\vec{R}$$ as a function of time $$t$$ is given by;
$$\overrightarrow{\mathrm{R}}=4 \sin (2 \pi \mathrm{t}) \hat{\mathrm{i}}+4 \cos (2 \pi \mathrm{t}) \hat{\mathrm{j}}$$
Where $$R$$ is in meters, $$t$$ is in seconds and $$\mathrm{\hat{i},\hat{j}}$$ denotes unit vectors along $$\mathrm{x}$$ and $$\mathrm{y}$$-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 $$4$$ m.
Subtopic:  Circular Motion |
60%
From NCERT
NEET - 2015
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A projectile is fired from the surface of the earth with a velocity of $$5$$ ms–1 and at an angle $$\theta$$ with the horizontal. Another projectile fired from another planet with a velocity of $$3$$ ms–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 |
71%
From NCERT
AIPMT - 2014
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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 |
83%
From NCERT
AIPMT - 2013
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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 |
75%
From NCERT
AIPMT - 2012
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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 |
80%
From NCERT
AIPMT - 2011
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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 |
76%
From NCERT
AIPMT - 2011
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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 |
83%
From NCERT
AIPMT - 2011
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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 |
From NCERT
AIPMT - 2011
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