# 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, $$\mathrm{sin}30^{0}=0.5$$ ) 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 $$\vec v$$ and acceleration $$\vec a.$$ Which of the following is true?
 1 $$\vec v$$ is a constant; $$\vec a$$ is not a constant 2 $$\vec v$$ is not a constant;  $$\vec a$$ is not a constant 3 $$\vec v$$ is a constant;   $$\vec a$$ is a constant 4 $$\vec v$$ is not a constant;    $$\vec a$$ is a constant
Subtopic:  Circular Motion |
53%
From NCERT
NEET - 2023
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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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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 $$\text{tan}^{-1}\Big(\frac{12}{37}\Big)$$ with respect to rain 2 $$\text{tan}^{-1}\Big(\frac{12}{37}\Big)$$ with respect to wind 3 $$\text{tan}^{-1}\Big(\frac{12}{35}\Big)$$ with respect to rain 4 $$\text{tan}^{-1}\Big(\frac{12}{35}\Big)$$ with respect to wind
Subtopic:  Relative Motion |
69%
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 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. $$\theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}$$
2. $$\theta=\sin ^{-1}\left(\frac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}$$
3. $$\theta=\cos ^{-1}\left(\frac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}$$
4. $$\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}$$

Subtopic:  Projectile Motion |
69%
From NCERT
NEET - 2021
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A car starts from rest and accelerates at $5$ $\mathrm{m}/{\mathrm{s}}^{2}$. At $$t=4$$ 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 $$t=6$$ s? (Take $$g=10$$ m/s2)
1. $20\sqrt{2}$
2. $20\sqrt{2}$ $\mathrm{m}/\mathrm{s},$ $10$ $\mathrm{m}/{\mathrm{s}}^{2}$
3. $20$ $\mathrm{m}/\mathrm{s},$ $5$ $\mathrm{m}/{\mathrm{s}}^{2}$
4. $20$ $\mathrm{m}/\mathrm{s},$ $0$

Subtopic:  Projectile Motion |
60%
From NCERT
NEET - 2021
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A particle moves along a circle of radius $${{20}\over{\pi}} m$$ 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. 640π ms–2

3. 160π ms–2

4. 40π ms–2

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