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Q. No.The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
| 1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |
| 3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |
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A stone projected with a velocity \(u\) at an angle \(\theta\) with the horizontal reaches maximum height \(H_1.\) When it is projected with velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches maximum height \(H_2.\) The relation between the horizontal range of the projectile \(R\) and \(H_1\) and \(H_2\) is:
| 1. | \(R=4 \sqrt{H_1 H_2} \) | 2. | \(R=4\left(H_1-H_2\right) \) |
| 3. | \(R=4\left(H_1+H_2\right) \) | 4. | \(R=\frac{H_1{ }^2}{H_2{ }^2}\) |
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An airplane is moving with a velocity \(u.\) It drops a packet from a height \(h.\) The time \(t\) taken by the packet to reach the ground will be:
1. \( \sqrt{\frac{2 g}{h}} \)
2. \( \sqrt{\frac{2 u}{g}} \)
3. \( \sqrt{\frac{h}{2 g}} \)
4. \( \sqrt{\frac{2 h}{g}}\)
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The equation of trajectory of a projectile is given by \(y = x-10x^{2}\). Its speed of projection is: (\(g =1 0\) m/)
1. \(1\) m/s
2. \(2\) m/s
3. \(3\) m/s
4. \(4\) m/s
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A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:
1. \(t=6\) s
2. \(t=7\) s
3. \(t=8\) s
4. \(t=14\) s
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1. \(\frac{2 \beta}{g}\)
2. \(\frac{2 \alpha}{g}\)
3. \(\frac{2 \alpha \beta}{g}\)
4. \(\frac{2 \alpha}{g \beta}\)
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When a particle is projected at some angle to the horizontal, it has a range \(R\) and time of flight \(t_1\). If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is \(t_2\), then:
1. \(t_{1} + t_{2} = \frac{2 R}{g}\)
2. \(t_{1} - t_{2} = \frac{R}{g}\)
3. \(t_{1} t_{2} = \frac{2 R}{g}\)
4. \(t_{1} t_{2} = \frac{R}{g}\)
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Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are \(v_{1} , v_{2}\) \(\text{and}\) \(v_{3}\) respectively, then:
1. \(v_{1} > v_{2} > v_{3}\)
2. \(v_{3} > v_{2} = v_{1}\)
3. \(v_{1} = v_{2} = v_{3}\)
4. \(v_{1} < v_{2} < v_{3}\)
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Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)
| 1. | The faster one |
| 2. | The slower one |
| 3. | Depends on masses |
| 4. | Both will reach simultaneously |
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Q. No.
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