A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be

1. 5  m

2. 4.8 m

3. 3.2 m

4. 3.0 m

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 boat is sent across a river in a perpendicular direction with a velocity of \(8\ \text{km/hr}\). If the resultant velocity of the boat is \(10\ \text{km/hr}\), then the velocity of the river is: 

1. \(10\ \text{km/hr}\)

2. \(8\ \text{km/hr}\) 

3. \(6\ \text{km/hr}\) 

4. \(4\ \text{km/hr}\) 

A boat is moving with a velocity of \(3\hat i+4 \hat j\) in the river, and the water is moving with a velocity of \(-3\hat i-4 \hat j\) with respect to the ground. The relative velocity of the boat with respect to the water is: 

1. \(-6\hat i-8 \hat j\)$$

2. \(6\hat i+8 \hat j\)$\mathrm{}$

3. \(8 \hat j\)$\mathrm{}$

4. \(6 \hat j\)$\mathrm{}$

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

1. \(5\ \text{min}\)

2. \(60\ \text{min}\)

3. \(20\ \text{min}\)

4. \(30\ \text{min}\)