1. | perpendicular to each other. |
2. | parallel to each other. |
3. | inclined to each other at an angle of \(45^\circ\). |
4. | antiparallel to each other. |
Four bodies \(P\), \(Q\), \(R\) and \(S\) are projected with equal velocities having angles of projection \(15^{\circ},\) \(30^{\circ},\)\(45^{\circ},\) and \(60^{\circ}\) with the horizontal respectively. The body having the shortest range is?
1. | \(P\) | 2. | \(Q\) |
3. | \(R\) | 4. | \(S\) |
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 \(\frac{\pi}{2}-\theta\) with the horizontal, it reaches maximum height \(H_2\). The relation between the horizontal range of the projectile \(R\) and \(H_1\) & \(H_2\) 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. | \(R=\frac{H_1{ }^2}{H_2{ }^2}\) |
A cricketer can throw a ball to a maximum horizontal distance of \(100~\text{m}\). With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is:
1. \(100~\text{m}\)
2. \(80~\text{m}\)
3. \(60~\text{m}\)
4. \(50~\text{m}\)
The horizontal range of a projectile is \(4 \sqrt{3}\) times its maximum height. Its angle of projection will be:
1. \(45^{\circ}\)
2. \(60^{\circ}\)
3. \(90^{\circ}\)
4. \(30^{\circ}\)
A boat is moving with a velocity \(3\hat i + 4\hat j\) with respect to ground. The water in the river is moving with a velocity\(-3\hat i - 4 \hat j\) with respect to ground. The relative velocity of the boat with respect to water is:
1. \(8\hat j\)
2. \(-6\hat i-8\hat j\)
3. \(6\hat i+8\hat j\)
4. \(5\sqrt{2}\)
A river is flowing from east to west at a speed of \(5\) m/min. A man on south bank of river, capable of swimming \(10\) m/min in still water, wants to swim across the river in shortest time. He should swim:
1. | Due north |
2. | Due north-east |
3. | Due north-east with double the speed of the river |
4. | None of the above |
A man sitting in a bus travelling in a direction from west to east with a speed of \(40\) km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear:
1. | To fall vertically downwards |
2. | To fall at an angle going from west to east |
3. | To fall at an angle going from east to west |
4. | The information given is insufficient to decide the direction of the rain |
A steam boat goes across a lake and comes back (a) On a quiet day when the water is still and (b) On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both the days was the same, in which case will the steam boat complete the journey in lesser time:
1. | Case (a) |
2. | Case (b) |
3. | Same in both case |
4. | Nothing can be predicted based on given data |
Two particles having position vectors \(\overrightarrow{r_{1}} = \left( 3 \hat{i} + 5 \hat{j}\right)\) metres and \(\overrightarrow{r_{2}} = \left(- 5 \hat{i} - 3 \hat{j} \right)\) metres are moving with velocities \(\overrightarrow{v}_{1} = \left( 4 \hat{i} + 3 \hat{j}\right)\)\(\text{m/s}\) and \(\overrightarrow{v}_{2} = \left(\alpha\hat{i} + 7 \hat{j} \right)\)\(\text{m/s}\). If they collide after \(2\) seconds, the value of \(\alpha\) is:
1. | \(2\) | 2. | \(4\) |
3. | \(6\) | 4. | \(8\) |