A cannon can give a maximum speed of \(70~\text{m/s}\) to bombs. The maximum distance up to which the cannon projects a bomb is: \((g=10~\text{m/s}^2)\)

1. \(490~\text m\)

2. \(245~\text m\)

3. \(100~\text m\)

4. \(300~\text m\)

A man is running horizontally at a velocity of 6 m/s while rain is falling vertically at 6 m/s. The rain strikes the man with a speed of

(1) 6$\sqrt{2}$ m/s

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

(3) 6 m/s

(4) 18 m/s

A man wants to cross a river 600 m wide flowing at 8 m/s in the shortest time. Man has a speed of 6 m/ s in still water. What is the path length covered by the man in the river?

1. Infinite

2. 1 km

3. 100 m

4. 1000 cm

The trajectory of a projectile in the vertical plane is y = ax - ${\mathrm{bx}}^2$ where a and b are constants, x and y are horizontal and vertical displacements from point of projection. The angle of projection from the horizontal is

1.  ${\tan }^{-1} \left(\frac{\mathrm{a}}{\mathrm{b}}\right)$

2.  ${\tan }^{-1} \left(\mathrm{b}\right)$

3.  ${\tan }^{-1} \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$

4.  ${\tan }^{-1} \left(\mathrm{a}\right)$

A shell is fired vertically upward with a velocity of \(20\) m/s from a trolley moving horizontally with a velocity of \(10\) m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: (\(g= 10~\text{m/s}^2\)${\mathrm{}}^{}$)

A car is moving at a speed of 30 m/s on a horizontal circular track of radius of 300 m. This speed is increasing at a rate of 4 $\mathrm{m}/{\mathrm{s}}^2$. Total acceleration of the car is:

(1) 5 $\mathrm{m}/{\mathrm{s}}^2$

(2) 7 $\mathrm{m}/{\mathrm{s}}^2$

(3) 1 $\mathrm{m}/{\mathrm{s}}^2$

(4) 3 $\mathrm{m}/{\mathrm{s}}^2$

A particle is moving along a circular path of radius a with constant angular velocity $\mathrm{\omega }$. The magnitude of displacement of the particle as a function of time t is:

1.  $\mathrm{a} \cos \mathrm{\omega t}$

2.  $\mathrm{a} \cos \frac{\mathrm{\omega t}}{2}$

3.  $\mathrm{a} \sin {\mathrm{\omega t}}^2$

4.  $2\mathrm{a} \sin \frac{\mathrm{\omega t}}{2}$

A projectile starts with speed u at an angle $\mathrm{\theta }$ from the horizontal ground. The average velocity of the projectile between the point of projection and the point of arrival on the ground is:

(1) usin$\mathrm{\theta }$

(2) 2usin$\mathrm{\theta }$

(3) ucos$\mathrm{\theta }$

(4) 2ucos$\mathrm{\theta }$

A projectile is thrown with speed 50 m/s at an angle 53° with the horizontal. Taking horizontal as x-axis and vertical as y-axis, the equation of trajectory of the projectile is

(1) 180y = 140x - ${\mathrm{x}}^2$

(2) 180y = 240x - ${\mathrm{x}}^2$

(3) 180y = 90x - 2${\mathrm{x}}^2$

(4) 180y = 80x - 3${\mathrm{x}}^2$

Time of flight of a body dropped from a height H is T. If another body is projected horizontally with speed v from the same height, then its time of flight will be:

1.  T

2.  $\mathrm{T}+\frac{\mathrm{H}}{\mathrm{v}}$

3.  $\mathrm{T}-\frac{\mathrm{H}}{\mathrm{v}}$

4.  $\sqrt{{\mathrm{T}}^2+\frac{{\mathrm{H}}^2}{{\mathrm{v}}^2}}$