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Q. No.
A bullet is fired from a gun at the speed of \(280~\text{ms}^{-1}\) in the direction \(30^\circ\) above the horizontal. The maximum height attained by the bullet is:\(\left(g=9.8~\text{m/s}^{2}, \sin30^{\circ}=0.5\right)\)
1. \(3000~\text{m}\) 2. \(2800~\text{m}\)
3. \(2000~\text{m}\) 4. \(1000~\text{m}\)
Subtopic:  Projectile Motion |
 67%
Level 2: 60%+
NEET - 2023
Hints
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 metres. Find the magnitude and direction of the velocity \(v(t)\), at \(t=1~\text{s},\) with respect to the \(x\text-\)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 |
 81%
Level 1: 80%+
NEET - 2023
Hints
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 |
 71%
Level 2: 60%+
NEET - 2023
Hints
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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 |
 66%
Level 2: 60%+
NEET - 2023
Hints
A ball is projected with a velocity of \(10~\text{m/s}\) at an angle of \(60^\circ\) with the vertical direction. Its speed at the highest point of its trajectory will be:
1. \(10~\text{m/s}\)
2. zero
3. \(5\sqrt{3}~\text{m/s}\)
4. \(5~\text{m/s}\)
Subtopic:  Projectile Motion |
 61%
Level 2: 60%+
NEET - 2022
Hints

Rain is falling vertically downward with a speed of \(35~\text{m/s}.\) The wind starts blowing after some time with a speed of \(12~\text{m/s}\) in the east to the 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 |
 71%
Level 2: 60%+
NEET - 2022
Hints
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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 |
 76%
Level 2: 60%+
NEET - 2022
Hints

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 |
 64%
Level 2: 60%+
NEET - 2021
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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 |
 71%
Level 2: 60%+
NEET - 2021
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The speed of a swimmer in still water is \(20~\text{m/s}.\) The speed of river water is \(10~\text{m/s}\) and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north is given by:

1. \(45^{\circ}\) west of north 2. \(30^{\circ}\) west of north
3. \(0^{\circ}\) west of north 4. \(60^{\circ}\) west of north
Subtopic:  Relative Motion |
 73%
Level 2: 60%+
NEET - 2019
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