Kinematics-07-PROBLEMS

LEVEL - IV 1. On a frictionless horizontal surface, assumed to be the x-y plane, a small y trolley A is moving along a straight line parallel to the y-axis (see figure) with A a constant velocity of  3  1 m/s. At a particular instant, when the line OA makes an angle of 45º with the x-axis, a ball is thrown along the surface from the origin O. Its velocity makes an angle  with the x-axis and it hits the trolley. O 45º x (a) The motion of the ball is observed from the frame of the trolley. Calculate the angle  made by the velocity vector of the ball with the x-axis in this frame. (b) Find the speed of the ball with respect to the surface, if   4 / 3 . 2. A large heavy box is sliding without friction down a smooth plane of inclination  . From a point P on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is u and the direc- tion of projection makes an angle  with the bottom as shown in the figure: (a) Find the distance along the bottom of the box between the point of P and the point Q where the particle lands (Assume that the particle does not hit any other surface of the box. Neglect air resistance.] (b) If the horizontal displacement of the particle as seen by an observer on the ground is zero, find the speed of the box with respect to the ground at the instant when the particle was projected. 3. Two guns situated on the tope of a hill of height 10m fire one shot each with the same speed 5 3m / s m/s at some interval of time. One gun fires horizontally and other fires upwards at an angle of 60º with the horizontal. The shots collide in air at point P. Find : (a) The time interval between the firings and (b) The coordinates of the point P. Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in x-y plane. 4. Two towers AB and CD are situated at a distance d apart as shown in C figure. AB is 20 m high and CD is 30 m high from the ground. An object of mass m is thrown from the top of AB horizontally with a velocity of 10 m/s towards CD. Simultaneously, another object of mass 2 m is thrown from the top of CD at an angle of 60º to the horizontal towards AB with the same A magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane collide is mid-air. Calculate the distance ‘d’ be- tween the towers. B D 5. A particle is moving along the x-axis under the accelerationa(x)   m and its velocity is v = 0; (a) Find its velocity when it reaches x = 0.5 . (b) Find the time at which it reaches x = 0.5 m. 1 2x 2 . At time t =0. it is at x = 1.0

Comments

Post a Comment

Popular posts from this blog

Physics-31.Rotational Mechanics

5.1 DEFINITION OF CENTRE OF MASS Centre of mass: Every physical system has associated with it a certain point whose motion characterizes the motion of the whole system. When the system moves under some external forces than this point moves as if the entire mass of the system is concentrated at this point and also the external force is applied at his point of translational motion. This point is called the centre of mass of the system. Centre of mass of system of n point masses or n particles is that point about which moment of mass of the system is zero, it means that if about a particular origin the moment of mass of system of n point masses is zero, then that particular origin is the centre of mass of the system. The concept of centre of mass is a pure mathematical concept. If there are n particles having mass m1, m2 ….m n and are placed in space (x1, y1, z1), (x2, y2, z2) ……….(x n, y n, z n) then centre of mass of system is defined as (X, Y, Z) where = Y = and Z = where
Read more

Physics-30.24-Physics-Solids and Semiconductors

UNIT 24 - SOLIDS AND SEMICONDUCTORS 1. SOLID STATE ELECTRONICS (SEMICONDUCTORS) (A) Energy bands in solids: (i) In solids, the group of closely lying energy levels is known as energy band. (ii) In solids the energy bands are analogous to energy levels in an atom. (iii) In solids the atoms are arranged very close to each other. In these atoms there are discrete energy levels of electrons. For the formation of crystal these atoms come close together, then due to nucleus-nucleus, electron-electron and electron-nucleus interactions the discrete energy levels of atom distort and consequently each energy level spits into a large number of closely lying energy levels. (iv) The number of split energy levels is proportional to the number of atoms interacting with each other. If two atoms interact then each energy level splits into two out of which one will be somewhat above and another will be somewhat below the main energy level. In solids the number of atoms is very large ( 1023). Hence eac
Read more

Planning to start your own coaching institute for JEE, NEET, CBSE or Foundation? Here's why not to waste time in developing study material from scratch. Instead use the readymade study material to stay focused on quality of teaching as quality of teaching is the primary job in coaching profession while study material is secondary one. Quality of teaching determines results of your coaching that decides success & future of your coaching while good quality study material is merely a necessary teaching aid that supplements your teaching (video in Hindi)

Image
Read more