![]() When the body returns to the ground, the net vertical displacement made by the projectile Let tf be the time of flight (i.e) the time taken by the projectile to reach B from O through A. Substituting the known values 0 = u sin θ – g t Let t be the time taken by the projectile to attain its maximum height. In the above Motion of a projectile projected at an angle with horizontal Fig, EA is the maximum height attained by the projectile. The maximum vertical displacement produced by the projectile is known as the maximum height reached by the projectile. Resultant velocity of the projectile at any instant t1Īt C, the velocity along the horizontal direction is ux = u cos θ and the velocity along the vertical direction is uy= u2. Thus the path of a projectile is a parabola. The above equation is of the form y = Ax + Bx2 and represents a parabola. Horizontal distance travelled by the projectile in time t1 is, x = horizontal velocity × time Let t1 be the time taken by the projectile to reach the point C from the instant of projection. After this, the vertical component uy is directed downwards and increases with time till the body strikes the ground at B. But the vertical component uy of the object continuously decreases due to the effect of the gravity and it becomes zero when the body is at the highest point of its path. The horizontal velocity ux of the object shall remain constant as no acceleration is acting in the horizontal direction. uy = u sin θ, along the vertical direction OY.ux = u cos θ, along the horizontal direction OX and.The velocity u can be resolved into two components Motion of a projectile projected at an angle with the horizontal (oblique projection)Ĭonsider a body projected from a point O on the surface of theĮarth with an initial velocity u at an angle θ with the horizontal as Thus the path taken by the projectile is a parabola. The above equation is the equation of a parabola. The velocity in the vertical direction shall go on changing because of acceleration due to gravity. The horizontal velocity of the object shall remain constant as no acceleration is acting in the horizontal direction. The two velocities are independent of each other. Vertical velocity, which is non-uniform due to acceleration due o gravity.Uniform velocity with which it is projected in the horizontal direction OX.The object acquires the following motions simultaneously : Let us consider an object thrown horizontally with a velocity u from a point A, which is at a height h from the horizontal plane OX (Fig below). Motion of a projectile thrown horizontally Time of flight is the total time taken by the projectile from the instant of projection till it strikes the ground. ![]() The path described by the projectile is called the trajectory. Range of a projectile is the horizontal distance between the point of projection and the point where the projectile hits the ground. The velocity with which the body is projected is known as velocity of projection. The angle between the initial direction of projection and the horizontal direction through the point of projection is called the angle of projection. In the study of projectile motion, it is assumed that the air resistance is negligible and the acceleration due to gravity remains constant. The resultant motion would be the vector sum of these two motions and the path following would be curvilinear. The above discussion can be summarised as in the Table below The object therefore has horizontal and vertical motions simultaneously. These two perpendicular components of motion are independent of each other. A body projected with an initial velocity making an angle with the horizontal direction possess uniform horizontal velocity and variable vertical velocity, due to force of gravity. The two components of the projectile motion are (i) vertical component and (ii) horizontal component. The projectiles undergo a vertical motion as well as horizontal motion. It can be thrown from the ground in a direction inclined to it.It can be projected horizontally from a certain height. ![]() Such a motion is known as projectile motion. A few examples of projectiles are (i) a bomb thrown from an aeroplane (ii) a javelin or a shot-put thrown by an athlete (iii) motion of a ball hit by a cricket bat etc. The different types of projectiles are shown in Fig. A body thrown with some initial velocity and then allowed to move under the action of gravity alone, is known as a projectile. If we observe the path of the projectile, we find that the projectile moves in a path, which can be considered as a part of parabola.
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