# Rain is falling vertically downward with a speed of $$35~\text{m/s}$$. Wind starts blowing after some time with a speed of $$12~\text{m/s}$$ in East to West direction. The direction in which a boy standing at the place should hold his umbrella is: 1.  $$\text{tan}^{-1}\Big(\dfrac{12}{37}\Big)$$ with respect to rain 2.  $$\text{tan}^{-1}\Big(\dfrac{12}{37}\Big)$$ with respect to wind 3.  $$\text{tan}^{-1}\Big(\dfrac{12}{35}\Big)$$ with respect to rain 4.  $$\text{tan}^{-1}\Big(\dfrac{12}{35}\Big)$$ with respect to wind

Subtopic:  Relative Motion |
69%
From NCERT
NEET - 2022
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A cricket ball is thrown by a player at a speed of $$20$$ m/s in a direction $$30^\circ$$ above the horizontal. The maximum height attained by the ball during its motion is: (Take $$g=10$$ m/s2)
1. $$5$$ m
2. $$10$$ m
3. $$20$$ m
4. $$25$$ m
Subtopic:  Projectile Motion |
73%
From NCERT
NEET - 2022
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A ball is projected with a velocity of $$10$$ ms–1 at an angle of $$60^\circ$$ with the vertical direction. Its speed at the highest point of its trajectory will be:
 1 $$10$$ ms–1 2 zero 3 $$5\sqrt3$$ ms–1 4 $$5$$ ms–1
Subtopic:  Projectile Motion |
59%
From NCERT
NEET - 2022
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A bullet is fired from a gun at the speed of $$280$$ ms–1 in the direction $$30^\circ$$ above the horizontal. The maximum height attained by the bullet is: ($$g=9.8$$ ms–2, $$\mathrm{sin}30^\circ=0.5$$ )
 1 $$3000$$ m 2 $$2800$$ m 3 $$2000$$ m 4 $$1000$$ m
Subtopic:  Projectile Motion |
61%
From NCERT
NEET - 2023
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The position of a particle is given by;
$$\vec r(t)=4t\hat i+2t^2\hat j+5\hat k$$
where $$t$$ is in seconds and $$r$$ in metre. Find the magnitude and direction of velocity $$v(t)$$, at $$t=1~\mathrm{s}$$, with respect to $$x$$-axis:
 1 $$4\sqrt2~\text{ms}^{-1},45^\circ$$ 2 $$4\sqrt2~\text{ms}^{-1},60^\circ$$ 3 $$3\sqrt2~\text{ms}^{-1},30^\circ$$ 4 $$3\sqrt2~\text{ms}^{-1},45^\circ$$
Subtopic:  Speed & Velocity |
77%
From NCERT
NEET - 2023
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A ball is projected from point $$A$$ with velocity $$20$$ ms–1 at an angle $$60^\circ$$ to the horizontal direction. At the highest point $$B$$ of the path (as shown in figure), the velocity $$v$$ (in ms–1) of the ball will be:

1. $$20$$
2. $$10\sqrt3$$
3. zero
4. $$10$$
Subtopic:  Projectile Motion |
67%
From NCERT
NEET - 2023
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A particle is executing uniform circular motion with velocity $$\overrightarrow v$$ and acceleration $$\overrightarrow a.$$ Which of the following is true?
 1 $$\overrightarrow v$$ is a constant; $$\overrightarrow a$$ is not a constant. 2 $$\overrightarrow v$$ is not a constant;  $$\overrightarrow a$$ is not a constant. 3 $$\overrightarrow v$$ is a constant;   $$\overrightarrow a$$ is a constant. 4 $$\overrightarrow v$$ is not a constant;    $$\overrightarrow a$$ is a constant.
Subtopic:  Circular Motion |
55%
From NCERT
NEET - 2023
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A particle moving in a circle of radius $$R$$ with a uniform speed takes a time $$T$$ to complete one revolution. If this particle were projected with the same speed at an angle $$\theta$$ to the horizontal, the maximum height attained by it equals $$4R.$$ The angle of projection, $$\theta$$ is then given by:

 1 $$\theta=\sin ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1/2}$$ 2 $$\theta=\sin ^{-1}\left(\dfrac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}$$ 3 $$\theta=\cos ^{-1}\left(\dfrac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}$$ 4 $$\theta=\cos ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}$$
Subtopic:  Projectile Motion |
69%
From NCERT
NEET - 2021
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A car starts from rest and accelerates at $$5~\text{m/s}^{2}$$. At $$t=4~\text{s}$$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $$t=6~\text{s}$$? (Take $$g=10~\text{m/s}^2)$$
1. $$20\sqrt{2}~\text{m/s}, 0~\text{m/s}^2$$
2. $$20\sqrt{2}~\text{m/s}, 10~\text{m/s}^2$$
3. $$20~\text{m/s}, 5~\text{m/s}^2$$
4. $$20~\text{m/s}, 0~\text{m/s}^2$$

Subtopic:  Projectile Motion |
61%
From NCERT
NEET - 2021
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A particle moves along a circle of radius $$\frac{20}{\pi}~\text{m}$$ with constant tangential acceleration. If the velocity of the particle is $$80$$ m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

1. $$40$$ ms–2

2. $$640\pi$$ ms–2

3. $$160\pi$$ ms–2

4. $$40\pi$$ ms–2

Subtopic:  Circular Motion |
56%
From NCERT
AIPMT - 2003
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