A ball is projected at an angle $\mathrm{\theta }$ with the horizontal. The angle of elevation of the ball when it is at the highest point is:

A particle is moving along a curve. Select the correct statement.

A man can row a boat with 8 km/h in still water. He is crossing a river of width 8 km, where the speed of water flow is 4 km/h. What direction should he head the boat to cross the river in the shortest time?

A particle is moving 30° north of east with speed 6 m/s. After 3 s the particle is found to be moving along north at the same speed. The magnitude of average acceleration in this interval of time is

A particle is thrown with a velocity of 40 m/s. If it passes A and B as shown in the figure at time ${\mathrm{t}}_1$ = 1 s and ${\mathrm{t}}_2$ = 3 s. The value of h is:

At a certain moment, the angle between the velocity vector $\overrightarrow{\mathrm{v}}$ and the acceleration $\overrightarrow{\mathrm{a}}$ of a particle is greater than 90°. What can be inferred about its motion at that moment?

To a stationary man, the rain is falling on his back with a velocity v at an angle $\mathrm{\theta }$ with vertical. To make the rain-velocity perpendicular to the man, he:

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:

A person can throw a ball up to a maximum horizontal range of 400 m. Maximum height to which he can throw the ball is:

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:

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 figure:

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:

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

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

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

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

A particle is thrown with velocity u making an angle $\mathrm{\theta }$ with the horizontal. It just crosses the top of two poles each of height h after 1 s and 3 s respectively. The time of flight of the particle is:

A projectile is moving in the XY plane such that the horizontal and vertical directions are along the X-axis and Y-axis respectively. The projectile is fired from the origin at a large height with initial velocity ($50\hat{\mathrm{i}} + 20\hat{\mathrm{j}}$) m/s. The time after which instantaneous velocity of the projectile becomes perpendicular to its initial velocity is:     (g=10m/s²)

A particle is thrown from the ground with a speed u at an angle $\mathrm{\theta }$ above the horizontal. The rate of change of velocity of the particle at the highest point of the path is:

A missile is fired for maximum range with an initial velocity of 20 m/s, then the maximum height of missile is

A particle is moving along a circle of radius R with constant speed ${\mathrm{v}}_0$. What is the magnitude of change in velocity when the particle goes from point A to B as shown?

An open trolley is moving on a horizontal road with constant velocity ${\mathrm{v}}_1$. A man on the trolley throws a ball vertically upward (with respect to trolley) with velocity ${\mathrm{v}}_2$. Select the correct statement.

Two stones are thrown simultaneously from the top of a building horizontally but in opposite directions, they will be moving perpendicular to each other say after time t, then t is equal to ___________. The initial speeds of stones are ${\mathrm{u}}_1 \mathrm{and} {\mathrm{u}}_2$ respectively and acceleration due to gravity is g.

Two projectiles projected with the same speed at angles $\mathrm{\theta }$ and (90° - $\mathrm{\theta }$) from the same point, then ${\mathrm{H}}_1 \times {\mathrm{H}}_2$ is equal to: (where symbols have their usual meanings)

A projectile is projected from the ground with speed 20 m/s at an angle 30° with vertical. The radius of curvature of the path of a projectile, when velocity makes 30° with horizontal is (g = 10 m/${\mathrm{s}}^2$)

A projectile is projected with speed u at an angle of 30° with the vertical from the ground. The angle between the acceleration of the projectile and its velocity at the time of striking the horizontal ground is:

Which of the following statements is incorrect?

A man is walking on a horizontal road with a speed of 4 km/h. Suddenly, the rain starts vertically downwards with a speed of 7 km/h. The magnitude of the relative velocity of the rain with respect to the man is:

A particle of mass 6 kg moves with an initial velocity of $\overrightarrow{\mathrm{v}} = \left(8\hat{\mathrm{i}} + 8\hat{\mathrm{j}}\right)$ m/s. A constant force of $\overrightarrow{\mathrm{F}}=-30\hat{\mathrm{j}}$ N is applied to the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle, when its y-coordinate again becomes zero is given by