Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the north to south direction. What is the direction in which she should hold her umbrella? [Given: tan 16º = 0.29 & tan 18º = 0.33]

1. 16º with the vertical, towards north

2. 18º with the vertical, towards north

3. 16º with the vertical, towards south

4. 18º with the vertical, towards south

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle at a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of the acceleration of the stone?
1. 8.1 ms^-2
2. 7.7 ms^-2
3. 8.7 ms^-2
4. 9.9 ms^-2

A particle starts from the origin at t = 0 sec with a velocity of $10$ $\hat{j}$ $m/s$ and moves in the x-y plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{-2}\). At what time is the x- coordinate of the particle 16 m?

A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of \(|displacement| \over distance\) will be:
1. 0
2. 1/7
3. 2/7
4. 1/11

Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of 5 m/s at an angle of \(120^\circ\) with the flow. The speed of the flow must be:
1. \(2.5\) m/s
2. \(3\) m/s
3. \(4\) m/s
4. \(1.5\) m/s

A car with a vertical windshield moves in a rain storm at a speed of \(40\) km/hr. The rain drops fall vertically with a constant speed of \(20\) m/s. The angle at which raindrops strike the windshield is:
1. ${\tan }^{-1}\frac{5}{9}$

2. ${\tan }^{-1}\frac{9}{5}$

3. ${\tan }^{-1}\frac{3}{2}$

4. ${\tan }^{-1}\frac{2}{3}$

A particle projected from origin moves in the x-y plane with a velocity $\overrightarrow{\mathrm{v}}=3\hat{\mathrm{i}}+6\mathrm{x}\hat{\mathrm{j}}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are the unit vectors along the x and y-axis. The equation of path followed by the particle is:

1. $\mathrm{y}={\mathrm{x}}^2$

2. $\mathrm{y}=\frac{1}{{\mathrm{x}}^2}$

3. $\mathrm{y}=2{\mathrm{x}}^2$

4. $\mathrm{y}=\frac{1}{\mathrm{x}}$

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $\mathrm{y}=(4\mathrm{t}-2{\mathrm{t}}^2)\mathrm{m}$ and $\mathrm{x}=\left(3\mathrm{t}\right)$ metre, where t is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:

1. $30°$

2. $37°$

3. $45°$

4. $60°$

The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection (u). Its range on the horizontal plane is:

1. $\frac{\sqrt{3}{\mathrm{u}}^2}{2\mathrm{g}}$

2. $\frac{3{\mathrm{u}}^2}{2\mathrm{g}}$

3. $\frac{3{\mathrm{u}}^2}{\mathrm{g}}$

4. $\frac{{\mathrm{u}}^2}{2\mathrm{g}}$