Note :

Rain, driven by the wind, falls on a railway compartment with a velocity of 20 ms−1, at an angle of 30◦ to the vertical. The train moves, along the direction of wind flow, at a speed of 108 kmh−1. Determine the apparent velocity of rain for a person sitting in the train.

A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45◦ with the horizontal and after 2s it is moving horizontally. What is the velocity of projection of the ball?

A ship A sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h, to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.

A particle moves in xy plane. The position vector at any time t is ~r = {(2t)iˆ + (2t2)ˆj} m. The rate of change of θ at time t = 2 second where θ is the angle which its velocity vector makes with positive x−axis) is

A projectile is given an initial velocity of (iˆ + 2ˆj)m/s, where iˆ is along the ground and ˆj is along the vertical. If g=10m/s2, the equation of its trajectory is

Referring to question−60, the ratio of speeds of striking for upward and downward projection is

A particle is moving eastwards with a velocity of 5 m/s. In 10 s, the velocity changes to 5 m/s northwards. The average acceleration in this time is

A particle is projected with a certain velocity at an angle a above the horizontal from the foot o an inclined plane of inclination 30◦ . If the particle strikes the plane normally, then α is equal to

A bird is flying towards north with a velocity 40 km h−1 and a train is moving with velocity 40 kmh−1 towards east. What is the velocity of the bird noted by a man in the train?

Two seconds after projection a projectile is travelling in a direction inclined at 30◦ to the horizontal after one more second, it is travelling horizontally, the magnitude and direction of its velocity are

A cat runs along a straight line with constant velocity of magnitude v. A dog chases the cat such that the velocity of dog is always directed towards the cat. The speed of dog is “u” and always constant. At the instant both are separated by distance x and their velocities are mutually perpendicular, the magnitude of acceleration of dog is.

A projectile is thrown in the upward direction making an angle of 60◦ with the horizontal direction with a velocity of 150 ms−1. Then the time after which its inclination with the horizontal is 45◦is

A particle is projected from a point O with a velocity u in a direction making an angle α upward with the horizontal. After some time at point P, it is moving at right angle with its initial direction of projection. The time of flight from O to P is

A particle is projected with a certain velocity at an angle an above the horizontal from the foot of an inclined plane of inclination 30◦ . If the particle strikes the plane normally, then a is equal to

Velocity of a particle at time t = 0 is 2 m/s. A constant acceleration of 2 m/s2 act on the particle for 2 s at an angle 60◦ with the initial velocity. The magnitude of velocity of particle at the end of 2 s will be

A man walks horizontally in rain with a velocity of 5 m/s. The raindrops strike on his back at angle of 45 with the horizontal.Then for the actual rain”s velocity

In horizontal level, ground to ground projectile if at any instant velocity becomes perpendicular to initial velocity, then what can you say about projection angle with horizontal?

AB is an inclined plane of inclination 30◦ with horizontal. Point O is 20 m above point A. A particle is projected horizontally from Oleftwards, and it collides with the plane AB perpendicularly. Speed of the particle at the time of projection should be g=10m/s²)

A body is projected up a smooth inclined plane (length = 20√ 2m ) with velocity u from the point M as shown in the figure. The angle of inclination is 45◦ and the top is connected to well of diameter 40m If the body just manages to cross the well, what is the value of v?

A very broad elevator plateform is going up vertically with a constant acceleration 1 ms-². At the instant when the velocity of the lift is 2 m/s, a stone is projected from the platform with a speed of 20 m/s relative to the floor at an elevation 30.The time taken by the stone to return to the floor will be,