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Saturday, 11 January 2020

PROJECTILE MOTION - TRAJECTORY EQUATION, DEFINITION AND FORMULAS

We were discussing the importance of friction i.e. positive and negative effects of frictionClassification of friction and Coulomb's law of dry friction with the help of our previous post.  

Now, we will be interested further to understand a very important topic in engineering mechanics i.e. projectile motion - trajectory equation, definition and formulas with the help of this post. We will find out here the basics of projectile motion, classification of projectile motion and various equations and formulas associated with the projectile motion. 

Let us first start here with the basic definition of projectile motion 

Projectile motion is basically defined as a motion where a particle moves in a vertical plane with some initial velocity but its acceleration will always be the free fall acceleration i.e. acceleration due to gravity which will be acting towards downward direction. 

When a particle will be thrown in to the space, it will have motion in x direction i.e. in horizontal direction and it will have motion in y direction too i.e. in vertical direction. 

The combination of motion of particle in x direction i.e. in horizontal direction and in y direction i.e. in vertical direction could be considered as the projectile motion. 

We must need to note it here that the horizontal motion and vertical motion of the particle in a projectile motion will be independent with each other. 

Let us consider that a particle is thrown in to the space with initial velocity u with an angle θ with the horizontal direction as displayed here in following figure. 


Following equations, as displayed below, will be used in order to determine the various desired formulas for a particle following the projectile trajectory. 


Where,
u = Initial velocity of the particle
V = Final velocity of the particle
a = Acceleration of the particle
t = Time of travel of the particle    

Above equations will be only valid for a particle which is under motion with constant acceleration.
In case of projectile motion, a i.e. acceleration of the particle will be basically acceleration due to gravity i.e. g and it will be acting towards downward direction. 

We will have following equations, as mentioned below, for particle motion in horizontal and in vertical direction. 


Projectile trajectory equation 

Above equation shows that it will be a parabolic equation and hence projectile motion trajectory will be parabolic. 

Time taken to reach the ground 

Time taken to reach the ground i.e. T will be determined with the help of following equation as mentioned below. 

Range or horizontal distance traveled by the particle

Range or horizontal distance traveled by the particle will be determined with the help of following equation as mentioned below. 

Maximum height or maximum vertical distance traveled by the particle

Maximum height or maximum vertical distance traveled by the particle will be determined with the help of following equation as mentioned below. 


Classification of projectile motion

Projectile motion will be basically classified in two types as mentioned here.
  1. Horizontal plane projectile motion
  2. Inclined plane projectile motion 

If we have a problem or a case of projectile motion where the point of projection and point of striking both are on inclined plane, we will say such projectile motion as inclined plane projectile motion.
Otherwise, we will say horizontal plane projectile motion. 

We must note it here very clearly that for inclined plane projectile motion, the point of projection and point of striking both must be on inclined plane. 

Therefore, we have studied here the basics of projectile motion, classification of projectile motion, equations associated with projectile motion, time of flight, range and maximum height traveled by the particle in a projectile motion with the help of this post. 

Further we will find out another concept in engineering mechanics i.e. terminal velocity and its expression with the help of our next post.  

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com.  

We will find out now the terminal velocity and its expression in our next post.  

Reference:  

Engineering Mechanics, By Prof K. Ramesh  
Image courtesy: Google    

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