# A Particle Is Projected Vertically Upwards

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## Particles Traveling Vertically Upwards: An Introduction to Kinematics

Particle kinematics is the study of the motion of objects in one-, two-, or three-dimensional space. It is a branch of classical mechanics that deals with describing the motion of objects and solving problems related to the motion of particles. When a particle is projected vertically upwards, its motion is called projectile motion and is a very important topic in kinematics. This article will introduce the concept of projectile motion and explain how it works.

### What Is Projectile Motion?

Projectile motion is the motion of an object that is projected into the air and then follows a curved path due to the force of gravity. If an object is projected with some initial velocity and no other forces act on it, then its path will be a parabola. This is because the acceleration due to gravity is constant and acts in a downward direction.

### Types of Projectiles

There are two types of projectile motion: horizontal and vertical. In horizontal projectile motion, the object is projected at an angle to the horizontal and follows a curved path. In vertical projectile motion, the object is projected vertically upwards and follows a parabolic path.

### Equations of Motion

The equations of motion for a particle projected vertically upwards are the same as those for any other type of projectile motion. The equations are expressed as a set of three equations: the equation of motion, the equation of conservation of energy, and the equation of conservation of momentum. The equations of motion for a particle projected vertically upwards are:
• The equation of motion: v = v0 + at, where v is the velocity, v0 is the initial velocity, a is the acceleration due to gravity and t is the time.
• The equation of conservation of energy: E = mgh, where E is the energy, m is the mass of the particle, g is the acceleration due to gravity, and h is the height of the particle.
• The equation of conservation of momentum: p = mv, where p is the momentum, m is the mass of the particle and v is the velocity.

### Examples of Projectiles

Projectiles can be seen in many everyday situations. Examples of projectiles include a ball thrown into the air, a rocket launching into space, a stone being thrown off a cliff, and a basketball being shot at a hoop. All of these examples involve the motion of a particle projected vertically upwards and can be described using the equations of motion.

### Applications of Projectile Motion

Projectile motion is used in many fields, from engineering to physics to astronomy. In engineering, it is used to calculate the trajectory of rockets and other projectiles. In physics, it is used to analyze the motion of objects in one-, two-, and three-dimensional space. In astronomy, it is used to calculate the orbits of planets and other celestial bodies.

### Conclusion

Projectile motion is a very important topic in kinematics. It involves the motion of an object that is projected with some initial velocity and follows a curved path due to the force of gravity. The equations of motion for a particle projected vertically upwards are the same as those for any other type of projectile motion. Projectile motion is used in many fields and can be seen in everyday situations, such as a ball thrown into the air or a basketball shot at a hoop. With a thorough understanding of projectile motion, it is possible to calculate the trajectory of objects and solve problems related to their motion.