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 man can swim at a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? 

1. 20 min
2. 18 min
3. 15 min
4. 16 min

In a harbor, the wind is blowing at the speed of 72 km/h, and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?

(1) Almost due north

(2) Almost due east

(3) Almost due west

(4)Almost due south

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall?

(1) 150.5 m

(2) 165.6 m

(3) 145.3 m

(4) 158.2 m

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

Which one of the following is not true?

1. The net acceleration of a particle in a circular motion is always along the radius of the circle towards the center.

2. The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.

3. The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

4. None of the above.

The position of a particle is given by,\(\overrightarrow{\mathrm{r}}=(3.0 \mathrm{t} \hat{\mathrm{i}}-2.0 \mathrm{t}^2 \hat{\mathrm{j}}+4.0 \hat{\mathrm{k}} )\mathrm{m}\) where t is in seconds and the coefficients have the proper units for $\stackrel{}{}$\(\vec{r}\) to be in meters. What is the magnitude and direction of the velocity of the particle at t = 2.0 sec?
1. \(7.56 \mathrm{~m} \mathrm{s}^{-1},-70^{\circ}\text{ with} ~\mathrm{y}- \text{axis}. \)
2. \(7.56 \mathrm{~m} \mathrm{s}^{-1}, ~70^{\circ}\text{ with} ~\mathrm{x}- \text{axis}. \)
3. \(8.54 \mathrm{~m} \mathrm{s}^{-1},~70^{\circ}\text{ with} ~\mathrm{y}- \text{axis}. \)
4. \(8.54 \mathrm{~m} \mathrm{s}^{-1},-70^{\circ}\text{ with} ~\mathrm{x}- \text{axis}. \)

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 $\left(8.0 \hat{i} +2.0 \hat{j}\right) m s^{-2}$. At what time is the x- coordinate of the particle 16 m?

1. 2 s

2. 3 s

3. 4 s

4. 1 s

$\hat{i} and \hat{j}$ are unit vectors along the x- and y-axis respectively. What is the magnitude and direction of the vector $\hat{i}-\hat{j}$?

(1) $\sqrt{2}, {45}^0 with x-axis.$

(2) $\sqrt{2}, -{45}^0 with x-axis.$

(3) $\frac{1}{\sqrt{2}}, {60}^0 with x-axis.$

(4) $\frac{1}{\sqrt{2}}, -{60}^0 with x-axis.$

For any arbitrary motion in space, which of the following relations is true?

$$\begin{gathered} \left(1\right) {\overrightarrow{\mathrm{v}}}_{\mathrm{avg}}=\left(\frac{1}{2}\right)\left[\overrightarrow{\mathrm{v}}\left({\mathrm{t}}_1\right)+\overrightarrow{\mathrm{v}}\left({\mathrm{t}}_2\right)\right] \\ \left(2\right) \overrightarrow{\mathrm{v}}\left(\mathrm{t}\right)=\overrightarrow{\mathrm{v}}\left(0\right)+\overrightarrow{\mathrm{a}}\mathrm{t} \\ \left(3\right) \overrightarrow{\mathrm{r}}\left(\mathrm{t}\right)=\overrightarrow{\mathrm{r}}\left(0\right)+\overrightarrow{\mathrm{v}}\left(0\right) \mathrm{t}+\frac{1}{2}\overrightarrow{\mathrm{a}} {\mathrm{t}}^2 \\ \left(4\right) {\overrightarrow{\mathrm{v}}}_{\mathrm{avg}}=\frac{\left[\overrightarrow{\mathrm{r}}\left({\mathrm{t}}_2\right)-\overrightarrow{\mathrm{r}}\left({\mathrm{t}}_1\right)\right]}{\left({\mathrm{t}}_2-{\mathrm{t}}_1\right)} \end{gathered}$$