A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30$$^\circ$$ above the horizontal. The maximum height attained by the ball du...

A ball is projected with a velocity, 10 ms$$-$$1, at an angle of 60$$^\circ$$ with the vertical direction. Its speed at the highest point of its traje...

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the sam...

A car starts from rest and accelerates at 5m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity an...

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60o with horizontal, it can travel a distance x1 along the pla...

A particle moving with velocity $$\overrightarrow V $$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :...

The x and y coordinates of the particle at any time are x = 5t $$-$$ 2t2 and y = 10t respectively, where x and y are in metres and t in seconds. The ...

In the given figure, a = 15 m s$$-$$2 represents the total acceleration of particle moving in the clockwise direction in a circle of radius R = 2.5 m ...

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

A particle moves so that its position vector is given by $$\overrightarrow r = \cos \omega t\,\widehat x + \sin \,\omega t\,\widehat y,$$ where $$\om...

If vectors $$\overrightarrow A = \cos \omega t\widehat i + \sin \omega t\widehat j$$ and $$\overrightarrow B = \cos {{\omega t} \over 2}\widehat i +...

The positions vector of a particle $$\overrightarrow R $$ as a function of time is given by $$\overrightarrow R $$ = 4sin(2$$\pi $$t)$$\widehat i$$ + ...

A ship A is moving Westwards with a speed of 10 km h$$-$$1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h$$-$$1. The tim...

A projectile is fired from the surface of the earth with a velocity of 5 m s$$-$$1 and angle $$\theta $$ with the horizontal. Another projectile fi...

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

Vectors $$\overrightarrow A ,\overrightarrow B $$ and $$\overrightarrow C $$ are such that $$\overrightarrow A .\overrightarrow B = 0$$ and $$\overri...

The velocity of a projectile at the initial point A is $$\left( {2\widehat i + 3\widehat j} \right)$$ m/s. It's 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 initial velocity $$\left( {2\overrightarrow i + 3\overrightarrow j } \right)$$ and acceleration $$\left( {0.3\overrightarrow i + 0.2\...

A projectile is fired at an angle of 45o with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of project...

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2$$\pi $$ s. The acceleration of the particle is

A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is

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

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

A particle moves in x-y plane according to rule x = asin$$\omega $$t and y = acos$$\omega $$t. The particle follows

A particle has initial velocity $$\left( {3\widehat i + 4\widehat j} \right)$$ and has acceleration $$\left( {0.4\widehat j + 0.3\widehat j} \right).$...

Six vectors, $$\overrightarrow a $$ through $$\overrightarrow f $$ have the magnitudes and directions indicated in the figure. Which of the following ...

A particle of mass m is projected with velocity v making an angle of 45o with the horizontal. When the particle lands on the level ground the magnitud...

A particle shows distance - time curve as given in this figure. The maximum instaneous velocity of the particle is around the point ...

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) planes. Its coordinates at a later time are $$\left( {\sqrt 3 ,3} \r...

$$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors and $$\theta $$ is the angle between them, if $$\left| {\overrightarrow A \times \...

For angles of projection of a projectile at angle (45o $$-$$ $$\theta $$) and (45o + $$\theta $$), the horizontal range described by the projectile ar...

The vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ are such that $$\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\ove...

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1...

If the angle between the vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ is $$\theta $$, the value of the product $$\left( {\overrightarrow...

If a vector $$2\widehat i + 3\widehat j + 8\widehat k$$ is perpendicular to the vector $$4\widehat j + 4\widehat i + \alpha \widehat k,$$ then the val...

If $$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \overrightarrow A .\overrightarrow B $$ then the value of $$\left| {\over...

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

A particle moves along a circle of radius $$\left( {{{20} \over \pi }} \right)$$ m with constants tangential acceleration. If the velocity of vthe pa...

A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5/sec from the same height then correc...

An object of mass 3 kg is at rest. Now a force of $$\overrightarrow F $$ = 6t2 $$\widehat i$$ + 4t $$\widehat j$$ is applied on the object then veloci...

If $$\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A } \right| + \left| {\overrightarrow B } \right|$$ then angle...

Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular veloci...

The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river in shortest time 15 min. Then the velocity of river s...

Two projectiles of same mass and with same velocity are thrown at an angle 60o and 30o with the horizontal, then which will remain same ...

A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revoluations in 44 s...