**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Terminology:Kinematics of a Particle

**Terminology:Kinematics of a Particle:**** ****Velocity of Projection**: The velocity with which the particle is projected is called as velocity of projection(in m/sec).

**Angle of Projection**: The angle between the direction of projection and horizontal direction is called as angle of projection(a).

**Trajectory**: The path traced by the projectile is called as its trajectory.

**Horizontal Range**: The horizontal distance through which the projectile travels in its flight is called the horizontal range.

**Time of flight**: The time interval during which the projectile is in motion is called time of flight.

We will study the case when the projectile flies over an inclined plane. A horizontal surface is a special case of an inclined plane.

Let *AB* be a plane inclined at an angle b to the horizontal as shown in the figure below. A projectile is fired up the plane from point *A* with initial velocity *u* m/sec and an angle a. Now, the range on inclined plane AB and the time of flight are to be determined

For the given projectile,

Integrating both equations with respect to time,

where *A _{1}* and

*A*are constants.

_{2}

Thus, *A _{1}*=

*u*sin(a-b)

and *A _{2}*=

*u*cos(a-b) Hence,