A body is thrown horizontally with a velocity $\sqrt{2 g h}$ from the top of a tower of height $h$. It strikes the level ground through the foot of the tower at a distance $x$ from the tower. The value of $x$ is:

Two men $P$ and $Q$ are standing at corners $A$ and $B$ of a square $ABCD$ of side $8~\text m.$ They start moving along the track with a constant speed $2~\text{m/s}$ and $10~\text {m/s}$ respectively. The time when they will meet for the first time is equal to:
       
1. $2~\text{sec}$
2. $3~\text{sec}$
3. $1~\text{sec}$
4. $6~\text{sec}$ 

A particle starts from the origin at t=0 and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is $y=b{x}^2$. The x component of its velocity (at t=0) is:

1. variable

2. $\sqrt{\frac{2a}{b}}$

3. $\frac{a}{2b}$

4. $\sqrt{\frac{a}{2b}}$

A body is projected with a velocity $u$ with an angle of projection $\theta.$ The change in velocity after the time $(t)$ from the time of projection will be:

What determines the nature of the path followed by the particle?

1. Speed only

2. Velocity only

3. Acceleration only

4. None of these

A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is : 

1. 10 km/hr

2. 8 km/hr

3. 6 km/hr

4. 4 km/hr

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. $6\hat{i}$

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip(returning to the initial point) is:

1. 5 min

2. 60 min

3. 20 min

4. 30 min

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south. 

1. 30° with downstream

2. 60° with downstream

3. 120° with downstream

4. South