Motion in a plane Questions
Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms⁻¹ collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other ?
A boy throws a ball into air at 45° from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ____ m. (g = 10 m/s²)
Velocity at maximum height of projectile is 1/2 of its initial velocity of projectile. Its angle of projection from the horizontal is
A ship is travelling due west at 40 km/h. Another ship has velocity 40 km/h 30° north to west w.r.t. first ship. The velocity of second ship is (in km/h)
Figure shows a quarter circle. A particle moves from B to O with 5 m/s, from O to A with 7 m/s. With what speed the particle should move from A to B so that average speed for total journey is 6 m/s?
If bullets are fired in all possible directions from same point with equal velocity of 10 ms-1 and with an angle of projection 45°, then the area covered by the bullets on the ground is nearly (Acceleration due to gravity = 10 ms–2)
A projectile crosses height 10 m twice with time gap 4 s. Find total time of flight (g = 10 m/s²).
A 20 g bead slides from rest along a circular wire of radius 10/π cm under constant tangential acceleration. If its kinetic energy reaches 10 mJ exactly upon completing its 5th revolution, find the magnitude of this tangential acceleration.
will be:
Two particles A and B are located in xy plane at points (0, 0) and (0, 4) m. They simultaneously start moving with velocities = 2 m/s and = 2 m/s. Select the correct statement
In a projectile motion from ground, let vx and vy are the horizontal and vertical components of velocity at any time t and x and y are displacements along horizontal and vertical from the point of projection at any time t. Then Statement A: vy - t gr
A particle is moving in xy plane such that its velocity in x-direction remains constant at 3 m/s and its velocity in y-direction varies with time as v = 2t m/s, where t is time in seconds. Displacement of particle at t = 3 s is (At t = 0, particle is
A person throws a stone in air at some angle. It is observed that after 2 s it is moving at an angle 30° to the horizontal and after further 2 s, it is travelling horizontally. The magnitude of initial velocity of stone is
A car, at origin, starts moving from rest on a horizontal ground such that the position vector of car with respect to its starting point is given as = 2t + 3t², equation of the trajectory of car is
A projectile is projected from ground, the horizontal range of the projectile is R and the maximum height attained by it is H. If a strong wind begins to blow now giving it a constant horizontal acceleration equal to g/3. Under the same conditions of
A man is running with velocity 20 km h⁻¹ towards west and rain is falling vertically down with 10 m s⁻¹. Direction of rain w.r.t. man is
A particle moves in space along the path z = ax³ + by² in such a way that = = c, where a, b and c are constants. The acceleration of the particle is
A 2 m wide truck is moving with a uniform speed v₀ = 8 m/s along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely
A particle moves in xy plane. The position vector of particle at any time t is = (2ti + 2t²j) m. The rate of change of θ at time t = 2 second is
A river is flowing with a velocity = 4i m/s. A boat is moving with a velocity BR = (−2i + 4j) m/s relative to river. The width of the river is 100 m along y-direction. Match column I with column II (in SI units)Column I Column II(A) Velocity of boat
A body is projected with certain velocity from ground. At a height of 0.4 m from the ground, the velocity of a body is = (6+ 2) m/s then the angle of projection from horizontal is (g = 10 m/s²)
A person of height 1.8 m is walking away from a lamp post of height 5 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is 70 cm s⁻¹, the speed of the tip of th
At the highest point in the path of a ground-to-ground oblique projectile
Given below are two statements: Statement I: A vector quantity has both, magnitude and direction and it must follow triangle law of addition. Statement II: If we multiply a vector A with a number λ then |λ| = λ||. In the light of the above statements
The ratio of possible maximum and minimum magnitudes of the resultant of two vectors and is 4 : 3. The relation between A and B is
Two car of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that they make complete circle in the same time t. The ratio of their centripetal acceleration is
In uniform circular motion, the centripetal acceleration has
A particle has initial velocity (4î + 6ĵ) m/s and a constant acceleration = (î + ĵ) m/s². The velocity of the particle after 2 second will be
Angular speed of a particle varies with time (in s) as ω = 4t² (rad/s). If the particle moves on a circular path of radius 1 m, then its tangential acceleration after 1 second will be
For a projectile thrown according to the situation given below; maximum height acquired by the projectile will be
A particle is moving on a circular track of radius 2 m. Its speed varies as v = αt² where α is a constant. The ratio of radial and tangential acceleration of particle at t = 2 s is
Position of a particle is varying with time as = a(t – 1)² î + bt² ĵ where ‘a’ and ‘b’ are constants. The time at which acceleration becomes normal to the velocity is
A swimmer crosses a river of width 500 m flowing at 4 km/h in minimum time. If his velocity in still water is 5 km/h then displacement along the river covered by him when he reaches opposite bank is
A particle moves in a circular path of radius 4 m with a uniform speed of 6 m/s. Its acceleration is
In uniform circular motion
Which of the following set of magnitude of vectors cannot give zero resultant?
Position vector of a particle moving in x-y plane is given by = 2tî + (3t – 6t²)ĵ. The equation of trajectory of the particle is
A stone is projected at an angle of 45° above the horizontal with speed 10√2 m/s from the top of a building of height 200 m. Taking the point of projection as origin, the position of particle after 3 s of projection will be (g = 10 m/s²)
Bullets from a gun fixed on ground at a point O have speed v directed at 45° from horizontal (as shown). The speed v such that it can just graze the top of a 2.4 m wall at a distance of 4 m from gun will be [Take g = 10 m/s²]
The angle of projection of a projectile for which range is double the maximum height, will be
Speed of a particle at the point of projection is times the speed at its maximum height. The angle of projection of projectile is
A particle starts from origin at t = 0 with velocity 6ĵ m/s in xy plane with constant acceleration of = (2î – 2ĵ) m/s². Position coordinates of the particle (in m) when velocity becomes parallel to x-axis is
A ball is dropped from a high tower at t = 0. After 10 s another ball is thrown in downwards direction from the same point with speed ‘v’. If these two balls meet at t = 15 s, then the value of ‘v’ is (Take g = 10 m/s²)
A bird is flying towards north with a velocity 40 kmh⁻¹ and a train is moving with constant velocity 40 km h⁻¹ towards east. What is the velocity of the bird relative to a man sitting in the train?
A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15S, then
Which of the following is NOT true regarding projectile motion? (g is the acceleration due to gravity and neglect air resistance)
A particle is thrown horizontally with speed u from height h. The magnitude of resultant velocity of the particle in air at any time t is;
The path followed by a body projected in x-y plane is y = (x − x²/2) m. The angle of projection of body with horizontal is (take g = 10 m/s²);
A man at rest observes the rain falling vertically. When he walks at 4 km/h, he has to hold his umbrella at an angle 53° from the vertical. Find the real velocity of raindrops.
A swimmer’s speed in the direction of flow of river as seen by observer on ground is 16 km/h. Swimmer’s speed against the direction of flow of river as seen by observer on ground is 8 km/h, then the swimmer’s speed in still water is;