explain what is projectile motion with diagram in brief and derive all equations for the projectile motion
Answers
Explanation:
What is Projectile Motion?
When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration that is directed towards the center of the earth (we assume that the particle remains close to the surface of the earth). The path of such particle is called a projectile and the motion is called as projectile motion. Air resistance to the motion of the body is to be assumed absent in projectile motion.
In a Projectile Motion, there are two simultaneous independent rectilinear motions:
Along x-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.
Along y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle.
Accelerations in the horizontal projectile motion and vertical projectile motion of a particle: When a particle is projected in the air with some speed, the only force acting on it during its time in the air is the acceleration due to gravity (g). This acceleration acts vertically downward. There is no acceleration in the horizontal direction which means that the velocity of the particle in the horizontal direction remains constant.
Parabolic Motion of Projectiles
Let us consider a ball projected at an angle θ with respect to horizontal x-axis with the initial velocity u as shown below:
Projectile Motion
The point O is called the point of projection; θ is the angle of projection and OB = Horizontal Range or Simply Range. The total time taken by the particle from reaching O to B is called the time of flight.
For finding different parameters related to projectile motion, we can make use of different equations of motions:
Projectile Motion
Total Time of Flight: Resultant displacement (s) = 0 in Vertical direction. Therefore, by using the Equation of motion:
gt2 = 2(uyt – sy) [Here, uy = u sin θ and sy = 0]
i.e. gt2 = 2t × u sin θ
Therefore, the total time of flight (t):
Projectile Motion
Horizontal Range: Horizontal Range (OA) = Horizontal component of velocity (ux) × Total Flight Time (t)
R = u cos θ × 2u×sinθg
Therefore in a projectile motion the Horizontal Range is given by (R):
Projectile Motion
Maximum Height: It is the highest point of the trajectory (point A). When the ball is at point A, the vertical component of the velocity will be zero. i.e. 0 = (u sin θ)2 – 2g Hmax [s = Hmax , v = 0 and u = u sin θ]
Therefore in a projectile motion the Maximum Height is given by (Hmax):
Projectile Motion
The equation of Trajectory: Let, the position of the ball at any instant (t) be M (x, y). Now, from Equations of Motion:
x = t × u cos θ . . . . . . (1)
y = u sin θ × t – 12×t2g. . . . . . (2)
On substituting Equation (1) in Equation (2):
Projectile Motion
This is the Equation of Trajectory in a projectile motion, and it proves that the projectile motion is always parabolic in nature.