Part -5 Motion in a plane hard

A body is projected at 30⁰angle with the horizontal with velocity 30 ms^–1. What is the angle with the horizontal after 1.5 s ? (Take g = 10 m s^–2)

A person standing on a truck moving with a uniform velocity 14.7 ms^–1 on a horizontal road throws a ball in such a way that it returns to him after 4s. Find the speed and angle of projection as seen by a man on the road -

A body is thrown from a point with speed 50 m/s at an angle 37⁰ with horizontal. When it has moved a horizontal distance of 80 m then it's distance from point of projection -

A circular disc of radius r = 5m is rotating in horizontal plane about y-axis. Y-axis is vertical axis passing through the centre of disc and x-z is the horizontal plane at ground. The height of disc above ground is h = 5 m. Small particles are ejecting tangentially from disc in horizontal direction with speed 12 m/s from the circumference of disc then the distance of these particles from origin when they hits the x-z plane is -

A projectile is thrown from origin in x - y plane with speed of 10 m/s at an angle 45º above positive x-axis where x-axis is horizontal axis, y-axis is vertical axis and origin is at ground. Assuming air resistance to be negligible and g = 10m/s² the minimum distance of projectile from a point P having coordinates (5m, 5m) is -

A baseball is thrown with an initial velocity of 100 m/s at an angle 30º above the horizontal. How far from the throwing point will it attain its original level?

A projectile is thrown into space so as to have maximum horizontal range R. Taking the point of projection as origin, the coordinates of the points where the speed of the particle is minimum are-

Two balls are projected from the same point in directions at 30⁰ and 60⁰ with the horizontal. Both the balls attain the same height.  The ratio of their velocities of projection is-

A bullet is fired horizontally with a velocity of 80m/s. During the first second -

For a projectile thrown into space with a speed v, the horizontal range is √3v²/2g . The vertical range is v²/8g .  The angle which the projectile makes with the horizontal initially is-

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is

A cannon and a target are 5.1 km apart located on the same level. Find the time to hit the target. Speed of cannot is 240 ms^-1. Assume no air drag.

A simple pendulum has a string of length l and bob of mass When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is

A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with a constant speed. What should be the minimum speed so that the water from the bucket does not spill out during rotation (g= 10 ms²)?

A toy car is tied to the end of an unstretched string of length When revolved, the toy car moves in a hori­zontal circle of radius 2a with time period T. If it is now revolved in a horizontal circle of radius 3a with a period T with the same force, then

A tube of length l is filled completely with an incom­pressible liquid of mass m and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is

A stone hanging from a massless string of length 15 m is projected horizontally with speed 147 m/s. Then the speed of the particle at the point where tension in string equals the weight of particle is –

A circular disc of radius r = 5 m is rotating in horizontal plane about y-axis. y-axis a vertical axis passing through the centre of disc and x-z is the horizontal plane at ground. The height of disc above ground is h = 5 m. Small particles are ejecting from disc in horizontal direction with speed 12 m/s from the circumference of disc then the distance of these particles from origin when they hits x – z plane is -

The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed ω varies with time t as –

An aeroplane flying horizontally with a speed of 360 km h^–1 releases a bomb at a height of 490 m from the ground. When will the bomb strike the ground?

A body is projected at angle 45⁰ to horizontal with velocity 20 m/s from ground. If there is an acceleration in horizontal direction of 2 m/s², then calculate horizontal range of this particle-

A particle is projected with a velocity of 20 m/s at an angle of 30⁰ to an inclined plane of inclination 30º to the horizontal. The particle hits the inclined plane at an angle 30⁰, during its journey. The time of flight is -

A ball rolls off the top of a stair way with a horizontal velocity of 4.5 m/s. If each step is 0.2 m high and 0.3 m broad, then the ball will strike the n^th step where n is equal to : (g = 10 m/s²)

The ceiling of a tunnel is of 5m high. What is the maximum horizontal distance that a ball thrown with a speed of 20 m/s, can go without hitting the ceiling of the tunnel ? (Take g = 10 m/s²)

An object is projected with a velocity of 20 m/s making an angle of 45⁰ with horizontal. The equation for the trajectroy is h = Ax – Bx² where h is height, x is horizontal distance. A and B are constants. The ratio A : B is : (g = 10 ms^–2)