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 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, \(\mathrm{sin}30^{0}=0.5\) )
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 \(\overrightarrow v\) 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 |
 54%
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. \( \theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\)
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 \(5~\text{m/s}^{2}\). 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 |
 60%
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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