## Saturday, March 4, 2017

### Motion of body in a Plane and Projectile motion Video Lesson

Any body moving in a plane where it has motion along horizontal and vertical directions, then the motion is called motion in a plane and it is also called two dimensional motion or projectile motion. For a body to have projectile motion, it shall be projected from the ground with an angle other than ninety  degree with a certain initial velocity.The body has sentimentally velocity along both the directions.  To find the velocity along a given direction, we need to resolve the initial velocity has to be resolved into components. Some component is along the horizontal axis and as there is no gravity along that direction and hence velocity component along the horizontal direction remains constant. The velocity along the vertical directions changes as acceleration due to gravity acts against initial vertical direction and hence the velocity keep changing along that direction. We can find the displacement along the horizontal and vertical directions. It is explained in the video lesson as shown in the video below.

Path of projectile is parabola

When a body is projected with an angle to the horizontal, it has displacement along both horizontal and vertical directions. We can find them using the equation of motion as shown in the diagram below. The displacement along X direction is independent of acceleration due to gravity as it is acting only along Y direction. We can find the time taken to have horizontal direction in terms of initial velocity as shown in the video lesson below. We can find the displacement along Y direction and we need to substitute the time from the first case and hence we will get a vertical displacement format as mathematical parabola.

Time of flight of Projectile

The time taken by the projectile to reach the ground from the point of projection is called time of flight. We need to know that by the time of end of journey, it comes to some other point on the ground and hence it has some horizontal displacement. But its initial and final position with respect to the Y direction and hence the vertical displacement by the end of time of flight along the vertical direction is zero. Taking this into consideration, we can find the time of flight as  shown in the video lesson below.

Velocity of Projectile at any instant

The projectile has some initial velocity and it can be resolved into components along horizontal and vertical direction. As the time progresses, the total velocity of the projectile changes. The horizontal component of velocity of the projectile remains constant but the vertical component of the velocity keeps on changing. To find the final velocity, we need to add final velocity components of X and Y directions and it can be done as shown in the video lesson below.

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