Question

Projectile motion derivation

Answer 1

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 & vertical direction of a particle in projectile motion: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.

Let us consider a ball projected at an angle θ with respect to horizontal x-axis with the initial velocity u as shown below:

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 differentequations of motions:

Answer 2

with a projective be thrown with a velocity u at angle W. Velocity projectile along the horizontal