When a man walks on a horizontal road with velocity 1 km/h, the rain appears to him coming vertically at a speed of 2 km/h. The actual speed of the rain w.r.t ground is:

Path of a projectile as seen from another projectile :

At an instant, the velocity and acceleration of a particle moving in the XY plane are $2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$ m/s and $-3\hat{\mathrm{i}}+2\hat{\mathrm{j}}$ $\mathrm{m}/{\mathrm{s}}^2$. Rate of change of speed of the particle at this instant is:

Which of the following statement/s is/are incorrect regarding the motion in a plane?

A body started moving with initial velocity 4 m/s along the east and acceleration 1 $\mathrm{m}/{\mathrm{s}}^2$ along the north. The velocity of the body just after 4 s will be

The radius vector of a particle moving on a circle is given by $\overrightarrow{\mathrm{r}} = \mathrm{AcosBt}\hat{\mathrm{i}} + \mathrm{AsinBtj}\stackrel{}{^}$ (A and B are constants). The radius of the circle and speed of the particle, respectively, are

For a particle projected on a horizontal surface, the ratio of range to maximum height is:

($\mathrm{\theta }$ is the angle of projection with respect to horizontal):

Two projectiles, one fired from the surface of the earth with speed 5 m/s and the other fired from the surface of a planet with initial speed 3 m/s with the same angle of the projection, trace identical trajectories. Neglecting friction effect, the value of acceleration due to gravity on the planet is:

A projectile is projected from origin of a co-ordinate system with initial velocity of $2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$ m/s considering y-axis along vertical. The equation of its trajectory is (take g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

During the downward motion of an oblique projectile from the top point of its trajectory, the radius of curvature of its trajectory will:

A particle is thrown obliquely at t = 0. The particle has the same K.E. at t = 5 seconds and at t = 9 seconds. The particle attains maximum altitude at:

A particle of mass m is thrown at t=0 with kinetic energy ${\mathrm{K}}_0$ at an angle 30° with the horizontal from the top of a tower of height 80 m. The particle again has kinetic energy ${\mathrm{K}}_0$ after time ${\mathrm{t}}_0$. The ${\mathrm{t}}_0$ is equal to:

The position vector of a particle is $\overrightarrow{\mathrm{r}} = \left(\mathrm{a} \sin \mathrm{\omega t}\right)\hat{\mathrm{i}} - \left(\mathrm{a} \cos \mathrm{\omega t}\right)\hat{\mathrm{j}}$. The velocity of the particle is:

Which of the following angles of projections will provide a maximum range to a projectile when projected with the same speed in all cases?

If a body is projected from the surface of the earth for maximum range R, then the maximum height attained by the body is:

A projectile is projected from the ground with the velocity ${\mathrm{v}}_0$ at an angle $\theta$ with the horizontal. What is the vertical component of the velocity of the projectile when its vertical displacement is equal to half of the maximum height attained?

The horizontal range of a particle thrown from the ground is four times the maximum height. The angle of projection with the vertical is:

A projectile is projected with a speed of 60 m/s at an angle of 60° from the horizontal. After some time projectile is moving at an angle of 30° with horizontal, what is the value of $\frac{\mathrm{d}}{\mathrm{dt}}\left|\overrightarrow{\mathrm{v}}\right|$ at this instant? (Given g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

A particle is rotating with increasing speed on a circular track. The angle between its radius vector and acceleration is $\theta$, then:

A particle starts moving on a circular path from rest, such that its tangential acceleration varies with time as ${\mathrm{a}}_{\mathrm{t}}$ = kt. Distance traveled by particle on the circular path in time t is

A projectile thrown from the ground has horizontal range R. If velocity at the highest point is doubled somehow, the new range will be:

The time of flights for a particle thrown for equal range at different angles is 4 sec and 3 sec. Speed of projection is:

A body is projected from the ground at a speed v at an angle $\mathrm{\theta }$ above the horizontal. The radius of curvature of its path at the highest point is:

A particle is projected from the origin with velocity $\left(4\hat{\mathrm{i}} + 9\hat{\mathrm{j}}\right)$ m/s. The acceleration in the region is constant and -10$\hat{\mathrm{j}}$ $\mathrm{m}/{\mathrm{s}}^2$. The magnitude of velocity after one second is

The speed of a boat in still water is half of the velocity of the flow of water(v). At what angle boat should steer with the direction of flow of water so that drift of boat is minimum?

A sports car is moving with a constant speed of 20 m/s on a horizontal road. Its motion is recorded by a camera, which is at 40 m from the road as shown. In order to focus the car, the camera is to be rotated at an angular speed equal to :

The magnitude of a vector $\overrightarrow{\mathrm{A}}$ is constant but it is changing its direction continuously. The angle between $\overrightarrow{\mathrm{A}}$ and $\frac{\mathrm{d}\overrightarrow{\mathrm{A}}}{\mathrm{dt}}$ is :

A particle is moving on a circular path of radius R. When the particle moves from point A to B (angle $\mathrm{\theta }$), the ratio of the distance to that of the magnitude of the displacement will be

Two particles move from A to C and A to D on a circle of radius R and diameter AB. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:
                                

A particle moves on the curve ${\mathrm{x}}^2 = 2\mathrm{y}$. The angle of its velocity vector with the x-axis at the point $\left(1, \frac{1}{2}\right)$ will be: