Q. No.A ball is thrown at an angle \(\theta_0\) above the horizontal, and follows the parabolic path taken by a projectile. Let its speed be \(v\) when its trajectory makes an angle \(\theta\) with the horizontal. Assuming \(A\) to be a constant,
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
Subtopic: Â Projectile Motion |
Level 4: Below 35%
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The average velocity of a projectile from the point of projection to impact is \(v_1\) while the average velocity from projection to maximum height\((H)\) is \(v_2\).
It can be concluded that:
It can be concluded that:
| 1. | \(v_1>v_2\) |
| 2. | \(v_1<v_2\) |
| 3. | \(v_1=v_2\) |
| 4. | Any of the above can be true depending on the angle of projection |
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
A projectile is launched at an angle \(\theta~(<90^{\circ})\) above the horizontal. Its velocity is measured along the direction of projection and is plotted against time and the magnitudes of the slopes are indicated in the figure below. Which of the following is the correct graph?
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
A projectile is fired from the top of a cliff, the maximum range of the projectile being \(1000\) m on level ground. The maximum range of the projectile, measured from the base of the cliff is:
| 1. | greater than \(1000\) m |
| 2. | less than \(1000\) m |
| 3. | equal to \(1000\) m |
| 4. | can be any of the above depending on the height of the cliff |
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
A ball is thrown up with a speed \(u\) at an angle of \(60^{\circ}\) with the horizontal; the thrower of the ball runs with a uniform speed \(v\) and stops suddenly when he reaches a certain point. He observes that the ball is at its maximum height, and then waits until it reaches him. Then
1. \(v=4u\)
2. \(v=2u\)
3. \(v=u\)
4. \(v<u\)
1. \(v=4u\)
2. \(v=2u\)
3. \(v=u\)
4. \(v<u\)
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
Two projectiles are fired simultaneously from the same point, one \((A)\)-vertically upward and the other \((B)\)-at some angle with the vertical. Both projectiles reach their maximum height above the ground simultaneously. Their separation at this instant is \(1600\) m. The range of the second projectile \((B)\) is:
1. \(2.4\) km
2. \(1.6\sqrt{3}\) km
3. \(1.6\sqrt2\) km
4. \(3.2\) km
1. \(2.4\) km
2. \(1.6\sqrt{3}\) km
3. \(1.6\sqrt2\) km
4. \(3.2\) km
Subtopic: Â Projectile Motion |
 62%
Level 2: 60%+
Hints
Particles are simultaneously projected in all possible directions from a point in space, located in a uniform gravitational field. The initial speed of the particle is \(u.\) The maximum separation between any two particles, after a time \(t,\) is:
| 1. | \(ut\) | 2. | \(2ut\) |
| 3. | \(ut+\dfrac{1}{2}gt^2\) | 4. | \(2ut+gt^2\) |
Subtopic: Â Projectile Motion |
 51%
Level 3: 35%-60%
Hints
A projectile projected close to the earth's surface rises to a maximum height of \(H\) and has a horizontal range of \(d\). The horizontal velocity of the projectile is:
| 1. | \(\sqrt{2gd} \) | 2. | \(\sqrt{2gH} \) |
| 3. | \(\sqrt{\dfrac{gd^2}{2H}} \) | 4. | \(\sqrt{\dfrac{gd^2}{8H}}\) |
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
A ball is thrown horizontally with a speed \(u\) from the top of a tall building and it impacts the ground at a horizontal distance which is equal to the height of the building. The height of the building is:
| 1. | \(\dfrac{u^2}{4g}\) | 2. | \(\dfrac{u^2}{2g}\) |
| 3. | \(\dfrac{2u^2}{g}\) | 4. | \(\dfrac{\sqrt2u^2}{g}\) |
Subtopic: Â Projectile Motion |
 53%
Level 3: 35%-60%
Hints
The acceleration of a projectile, in the direction of its motion:
| 1. | is always positive |
| 2. | is always negative |
| 3. | maybe positive, negative or zero |
| 4. | is always non-zero |
Subtopic: Â Projectile Motion |
 53%
Level 3: 35%-60%
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