Projectile Motion

DEFINITION:The motion of a body which is affected by only one force that is the force of gravity OR Projectile motion is the motion in which a body is given some initial velocity and then it is left to move under the force of gravity.


EXPLANATION:The only force which is acting on the projectile is the force of gravity which is the downward vertical in direction.We resolve the motion of the projectile into its components i.e the X-component and the Y-component{These components are the perpendicular to each other}.

If you see this image you will notice that the projectile starts a upward motion but then the initial velocity given to it is overcomed by the force of gravity and it starts the downward descent.The path followed by the projectile is called parabola which depends on the initial velocity or original velocity and the theta formed by the parabola with the horizontal component which is the X-axis.

There are different aspects to this motion like that of acceleration,time taken by the whole flight,Range,and the highest point reached by the projectile during its motion.There is no acceleration on the X-component because there is no force acting on the body along X-axis so we can say that according to newton’s first law when there is no force there is no acceleration and the body’s velocity will remain constant.

Force=0 then acceleration=o and velocity=constant [NEWTON'S FIRST LAW]

But gravity is acting on the Y-component so the acceleration will be equal to ‘g’ [acceleration due to gravity].Because the two components of a vector are independent of each other that is why Y-axis which is affected by gravity doesn’t affect the constant velocity of the X-axis.
the x-axis velocity remains constant.

RANGE:It is the horizontal distance covered by the projectile.It is governed by the velocity along X-axis which is always constant. R= (u2sin2Ø)/g is the formula for range in which u is the initial velocity squared along X-axis.Maximum range is attained by keeping the value of sine theta maximum in which initial velocity and ‘g’ are kept constant.If sin 2theta=1 then Range=maximum.
sin 2theta=sin 90 degrees2theta=90 degrees so, theta = 45 degreesThus projectile launched at 45 degrees will travel max range.

TIME OF FLIGHT:It is the total time taken by the projectile in the air. Its formula is T= (2usinØ)/g.

MAXIMUM HEIGHT:It is the maximum height reached by the projectile during its upward motion.It is on the half trip of the projectile that it reaches its maximum height.H= (u2sin2Ø)/2g is its formula in which u is the initial velocity squared and over here the sine theta is also squared.