A ball is projected with velocity v₀ at an angle of elevation 30°. Mark the correct statement.

Neglecting the air resistance, the time of flight of a projectile is determined by:

A stone is thrown at an angle θ with the horizontal reaches a maximum height of H. Then the time of flight of stone will be:

The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be 

The maximum horizontal range of a projectile is 400 m. The maximum value of height(ever possible) attained by it will be 

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

A man standing on a road holds his umbrella at 30° with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be:

A river is flowing from east to west at a speed of 5 m/min. A man on south bank of river, capable of swimming 10m/min in still water, wants to swim across the river in shortest time. He should swim:

A thief is running away on a straight road in a jeep moving with a speed of 9 m/s. A police man chases him on a motor cycle moving at a speed of 10 m/s. If the instantaneous separation of jeep from the motor cycle is 100 m, how long will it take for the policemen to catch the thief

A man sitting in a bus travelling in a direction from west to east with a speed of 40 km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear 

A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is 

A 120 m long train is moving towards west with a speed of 10 m/s. A bird flying towards east with a speed of 5 m/s crosses the train. The time taken by the bird to cross the train will be 

A boat crosses a river with a velocity of 8 km/h. If the resulting velocity of boat is 10 km/h, then the velocity of river water is 

A vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $\left|\Delta \overrightarrow{a}\right|$ and $\Delta a$ are respectively

A steam boat goes across a lake and comes back (a) On a quiet day when the water is still and (b) On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both the days was the same, in which case will the steam boat complete the journey in lesser time:

To a person, going eastward in a car with a velocity of 25 km/hr, a train appears to move towards north with a velocity of $25\sqrt{3}$ km/hr. The actual velocity of the train will be

An object is moving on a circular path of the radius r with constant speed v. The average acceleration of the object, after it has travelled three and a half rounds, is

Two particles having position vectors $\overrightarrow{r_1}=(3\hat{i}+5\hat{j})$ metres and $\overrightarrow{r_2}=(-5\hat{i}-3\hat{j})$ metres are moving with velocities ${\overrightarrow{v}}_1=(4\hat{i}+3\hat{j})m/s$ and ${\overrightarrow{v}}_2=(\alpha \hat{i}+7\hat{j})$ m/s. If they collide after 2 seconds, the value of ‘α’ is-

The x and y coordinates of the particle at any time are x=5t-2$t^2$ and y=10t respectively, where x and y are in the metres and t is in seconds. The acceleration of the particle at t=2s is :

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be 

A particle moves so that its position vector is given by $r=cos\omega t \hat{x}+sin\omega t \widehat{y }where \omega$ is a constant.  Based on the information given, which of the following is true?

A particle of mass 10g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8x10^-4 J by the end of the second revolution after the beginning of the motion?

A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle $\mathrm{\theta }$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m/s²) is: [Given, g = 9.8 m/s²]

A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (v_av) from t = 0 to t = 5s is

The velocity of a projectile at the initial point A is (2i + 3j) m/s. Its velocity (in m/s) at point B is:

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

A particle has an initial velocity (2i + 3j) and an acceleration (0.3i + 0.2j). The magnitude of velocity after 10s will be

A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is

A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 $\mathrm{m}/{\mathrm{s}}^2$, the range of the missile is:

A projectile is fired at an angle of 45$°$ with the horizontal. The elevation angle $\alpha$ of the projectile at its highest point as seen from the point of projection is: