Rain is falling vertically with a speed of $35~\text{ms}^{-1}$. Winds starts blowing after sometime with a speed of $12~\text{ms}^{-1}$ 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 $5.0\hat i~\text{m/s}$ 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 $84~\text m?$
1. $36~\text{m/s}$
2. $26~\text{m/s}$
3. $1~\text{m/s}$
4. Zero

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 $12~\text{cm}$ moves along the groove steadily and completes $7$ revolutions in $100~\text{s}.$ 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. $\text{no},$ $2.3~\text{cm/s}^2$