Rain is falling vertically downwards with a speed of \(4\) kmh^-1. A girl moves a straight road with a velocity of \(3\) kmh^-1 . The apparent velocity of rain with respect to the girl is:
1. \(3\) kmh^-1
2. \(4\) kmh^-1
3. \(5\) kmh^-1
4. \(7\) kmh^-1
 

Two bullets are fired horizontally and simultaneously towards each other from rooftops of two buildings 100 m apart and of the same height of 200 m, with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m/$s^2$)

1. after 2 sec at a height of 180 m.

2. after 2 sec at a height of 20 m.

3. after 4 sec at a height of 120 m.

4. they will not collide.

Ship \(A\) is travelling with a velocity of \(5~\text{km/h}\) due east. A second ship is heading $\mathrm{}$\(30^\circ\) east of north. What should be the speed of the second ship if it is to remain always due north with respect to the first ship?
1. \(10~\text{km/h}\)
2. \(9~\text{km/h}\)
3. \(8~\text{km/h}\)
4. \(7~\text{km/h}\)

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 the 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 boat is moving with velocity of $3\hat{i}+4\hat{j}$ in river and water is moving with a velocity of $-3\hat{i}-4\hat{j}$ with respect to ground. Relative velocity of boat with respect to water is: 

1. $-6\hat{i}-8\hat{j}$

2. $6\hat{i}+8\hat{j}$

3. $8\hat{j}$

4. $6\hat{i}$

The speed of water in a river is \(4~\text{km/h}\) and a man can swim at \(5~\text{km/h}.\) The minimum time taken by the man to cross the river of width \(200~\text m\) is:

1. \(\dfrac{1}{5}~\text h\)

2. \(\dfrac{1}{25}~\text h\)

3. \(\dfrac{1}{15}~\text h\)

4. \(\dfrac{1}{20}~\text h\)

The speed of a boat is \(5\) km/hr in still water. It crosses a river of width \(1\) km along the shortest possible path in \(15\) minutes. The velocity of the river water is:
1. \(3\) km/hr
2. \(4\) km/hr
3. \(5\) km/hr
4. \(2\) km/hr