A man is walking on the road with a speed \(3\) m/s. Rain is falling vertically at speed \(3\) m/s. At what angle from the vertical, man has to hold his umbrella to avoid the rain drops?
1. \(45^\circ\)
2. \(30^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)

A river is \(1\) km wide. The banks are straight and parallel. The current is \(5\) km/h and is parallel to the banks. A boat has a maximum speed of \(3\) km/h in still water. In what direction should the boat head so as to arrive at point \(B\) directly opposite to its starting point \(A\)?

A particle is projected with a velocity \(v\) such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is: (where \(g\) is acceleration due to gravity)

A man moving in the west direction observes wind is blowing towards the south. If the man doubles his speed in the same direction, then the direction of wind with respect to man will be:

1.  North-West

2.  South-West

3.  North-East

4.  East-South

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

A man standing on a road holds his umbrella at \(30^{\circ}\) with the vertical to keep the rain away. He throws the umbrella and starts running at \(10\) km/hr. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be:
1. \(10\) km/hr
2. \(20\) km/hr
3. \(30\) km/hr
4. \(40\) km/hr

A particle is projected from a horizontal plane (\(x\text-z\) plane) such that its velocity vector at time \(t\) is given by \(\vec{v}=a \hat{i}+(b-c t )\hat{j}\). Its range on this horizontal plane is given by: 

A man is crossing a river flowing with a velocity of \(5\) m/s. He reaches a point directly across the river at a distance of \(60\) m in \(5\) s. His velocity in still water should be:
1. \(12\) m/s
2. \(13\) m/s
3. \(5\) m/s
4. \(10\) m/s

A ball is projected at a certain angle with initial velocity \(u\). It covers horizontal range \(R\). With what initial velocity it should be projected keeping the angle of projection the same so that its horizontal range becomes \(2.25R\)?

A particle is moving with velocity \(\overrightarrow{v} = k \left(y \hat{i} + x \hat{j}\right)\) where \(k\) is a constant. The general equation for the path will be: