Rain is falling vertically with a speed of \(35~\text{ms}^{-1}\)${\mathrm{}}^{}$. Winds starts blowing after sometime with a speed of \(12~\text{ms}^{-1}\)${\mathrm{}}^{}$ in east to west direction. At what angle should a boy waiting at a bus stop hold his umbrella?

A motorboat is racing towards the north at \(25\) km/h and the water current in that region is \(10\) km/h in the direction of \(60^\circ\) east of the south. The resultant velocity of the boat is:

A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2\). What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84\) m?

Rain is falling vertically with a speed of \(35\) m/s. A woman rides a bicycle with a speed of \(12\) m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?

Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:

A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))

A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:
1. \(2.5\) s
2.  \(2.9\) s
3.  \(3.5\) s
4.  \(3\) s

An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion? 

An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. Is the acceleration vector a constant vector? What is its magnitude?
1. \(\text{yes},\) \(2.3~\text{cm/s}^2\)
2. \(\text{no},\) \(5.3~\text{cm/s}^2\)
3. \(\text{yes},\) \(5.3~\text{cm/s}^2\)
4. \(\text{no},\) \(2.3~\text{cm/s}^2\)