Have you ever observed that, When you kick a football it travels in a curved path. The particle that travels the curved path is called the projectile. The motion of projectile is called Projectile motion. The motion of the particle can be studied separately for horizontal and vertical parts. The point of projection is taken as origin.
For horizontal motion of the projectile,
x = v0 tcosθ
For vertical motion of the projectile,
y = (v0 sin θ)xt – ½gt2
Equation of Path of a Projectile
y = (tanθ)x – g x2 / (2 (v0cosθ)2)
This equation is in the form y = ax + bx2, where a and b are constants. This is the Equation of Parabola. It means that the Path of Projectile is a Parabola.
Time of Maximum Height
In projectile motion, the distance between the highest point and the ground is the maximum height.
tm= v0 sinθ/g
Time of Flight
The total time during which the projectile is in flight is called as the time of flight.
Tf = 2 (v0 sin θ) / g
Relation between tm and Tf
Tf = 2 tm
Maximum Height of a Projectile in Projectile Motion
The point at which the vertical component of velocity becomes zero is the Highest Point of the projectile. The distance of this point from the ground is called the Maximum Height. The projectile reach the maximum height at time of maximum height tm. The expression for Maximum Height of the Projectile is
hm = (v0 sin θ)2 / 2g
Horizontal Range of a Projectile
The horizontal distance covered by a projectile till it reaches the ground again after being projected is known as Horizontal range of a Projectile. It is denoted by R.
The value of Maximum Range will be given as
Rm = v02 /g
This article is helpful for Class 11 Physics
Keywords: Projectile motion, Projectile, Horizontal range of projectile, Time of Flight, Time of Maximum Height in Projectile Motion
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