The speed of a swimmer in still water is \(20\) m/s. The speed of river water is \(10\) 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 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

Two bullets are fired horizontally and simultaneously towards each other from rooftops of two buildings (building being 100 m apart and being 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 2s at a height of 180 m

2. after 2s at a height of 20 m

3. after 4s at a height of 120 m

4. they will not collide.

A ship A is moving Westwards with a speed of 10 kmph and a ship B 100 km South of A, is moving Northwards with a speed of 10 kmph. The time after which the distance between them becomes the shortest is:
1. 0 h
2. 5 h
3. $5\sqrt{2}$h
4. $10\sqrt{2}$h

Two particles A and B, move with constant velocities v₁ and v₂ respectively. At the initial moment, their position vectors are r₁ and r₂ respectively. The condition for particles A and B for their collision will be

1. $\frac{{\mathrm{r}}_1-{\mathrm{r}}_2}{\left|{\mathrm{r}}_1-{\mathrm{r}}_2\right|}=\frac{{\mathrm{v}}_2-{\mathrm{v}}_1}{\left|{\mathrm{v}}_2-{\mathrm{v}}_1\right|}$

2. ${\mathrm{r}}_1·{\mathrm{v}}_1={\mathrm{r}}_2·{\mathrm{v}}_2$

3. ${\mathrm{r}}_1\times {\mathrm{v}}_1={\mathrm{r}}_2\times {\mathrm{v}}_2$

4. ${\mathrm{r}}_1-{\mathrm{r}}_2={\mathrm{v}}_1-{\mathrm{v}}_2$

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v₁. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is -

1. $\frac{a}{\sqrt{v^2+v_1^2}}$

2. \(\frac{a}{\sqrt{v^{2}-v_{1}^{2}}}\)

3. $\frac{a}{(v-v_1)}$

4. $\frac{a}{(v+v_1)}$

The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river with the shortest possible path in 15 min. Then the velocity of river stream is :

1. 3 km/hr

2. 4 km/hr

3. $\sqrt{29}$ km/hr

4. $\sqrt{41}$ km/hr

Two particles are separated by a horizontal distance x as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. The time after which the horizontal distance between them becomes zero will be
                     
1.  $\frac{x}{u}$

2. $\frac{u}{2x}$

3.  $\frac{2u}{x}$

4. None of the above

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 river water is :
1. 3 km/hr
2. 4 km/hr
3. 5 km/hr
4. 2 km/hr