A particle is thrown from the ground with a speed of 20 m/s at an angle 60° above the horizontal. Average velocity over its entire journey just before hitting the ground is:

(1) 10 m/s

(2) 20 m/s

(3) Zero

(4) 15 m/s

A person can throw a ball up to a maximum horizontal range of \(400~\text{m}\). The maximum height to which he can throw the ball is:
1. \(200~\text{m}\)
2. \(100~\text{m}\)
3. \(150~\text{m}\)
4. \(250~\text{m}\)

A particle is moving on a circular path of radius 1 m with a speed of 10 m/s. The magnitude of change in its velocity in the interval it subtends an angle 60° at the center is:

1. 10 m/s

2. 20 m/s

3. $20\sqrt{2}$ m/s

4. Zero

A car is moving along east at 10 m/s and a bus is moving along north at 10 m/s. The velocity of the car with respect to the bus is along:

A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{\mathrm{v}}=4 \hat{\mathrm{i}}+2 \mathrm{t} \hat{\mathrm{j}}\). The trajectory of the particle is correctly shown in the figure:

1.		2.
3.		4.

A body A is projected vertically upwards. Another body B of the same mass is projected at an angle of 60° with the horizontal. If both the bodies attain the same maximum height, the ratio of the initial kinetic energy of body A to that of body B is:

1.  $\frac{3}{4}$

2.  $\frac{\sqrt{3}}{2}$

3.  $\frac{1}{\sqrt{2}}$

4.  $\frac{1}{2}$

Particles P and Q are at ${\overrightarrow{\mathrm{r}}}_{\mathrm{P}} = 3\hat{\mathrm{i}} + 2\hat{\mathrm{j}}$ and ${\overrightarrow{\mathrm{r}}}_{\mathrm{Q}} = 2\hat{\mathrm{i}} + \hat{\mathrm{j}}$. Their velocities at these positions are ${\overrightarrow{\mathrm{v}}}_{\mathrm{P}} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$ and ${\overrightarrow{\mathrm{v}}}_{\mathrm{Q}} = 3\hat{\mathrm{i}} + \mathrm{c}\hat{\mathrm{j}}$ respectively. If they collide after one second, then the value of c is

(1) 1

(2) 2

(3) 3

(4) 4

Two projectiles are thrown at different angles but their ranges R are the same. If their times of flight are ${\mathrm{t}}_1 \mathrm{and} {\mathrm{t}}_2$, then the product of their times of flight ${\mathrm{t}}_1{\mathrm{t}}_2$ is proportional to

1.  $\frac{1}{\mathrm{R}}$

2.  $\frac{1}{{\mathrm{R}}^2}$

3.  ${\mathrm{R}}^2$

4.  R

It is raining at 20 m/s in still air. Now a wind starts blowing with speed 10 m/s in the north direction. If a cyclist starts moving at 10 m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be

1. 20 m/s

2. $20\sqrt{2}$ m/s

3. $10\sqrt{5}$ m/s

4. 30 m/s

A body of mass 2 kg is projected at a speed of 20 m/s from a pillar of height 40 m at an angle of 30° with the horizontal in an upward direction. The speed with which it will hit the ground is

(1) 30 m/s

(2) 20$\sqrt{3}$ m/s

(3) 25 m/s

(4) 40 m/s