Constant in Projectile Motion: Horizontal Component of Velocity

Introduction:
Projectile motion refers to the motion of an object that is launched into the air and influenced only by the force of gravity and air resistance. It is a two-dimensional motion involving both horizontal and vertical components. In projectile motion, several quantities change throughout the motion, but there is one quantity that remains constant. Let's discuss the options given in the question and find the correct answer.

Options:
a) Resultant of the velocity of projection: The resultant velocity of projection is the vector sum of the horizontal and vertical components of velocity. As the object moves through its trajectory, the magnitude and direction of the resultant velocity change continuously. Therefore, the resultant of the velocity of projection is not constant in projectile motion.

b) Vertical component of the velocity: The vertical component of velocity represents the speed at which the object is moving vertically. In projectile motion, the vertical component of velocity changes continuously due to the influence of gravity. As the object moves upward, the vertical component decreases, and as it moves downward, the vertical component increases. Therefore, the vertical component of the velocity is not constant in projectile motion.

c) Horizontal component of the velocity: The horizontal component of velocity represents the speed at which the object is moving horizontally. In projectile motion, the horizontal component of velocity remains constant throughout the motion. This is because no horizontal force acts on the object, and there is no acceleration in the horizontal direction. Therefore, the horizontal component of the velocity is constant in projectile motion.

d) Velocity of projection: The velocity of projection is the initial velocity with which the object is launched. In projectile motion, the velocity of projection remains constant if there are no external forces acting on the object after its launch. However, as the object moves through its trajectory, the velocity changes due to the influence of gravity. Therefore, the velocity of projection is not constant in projectile motion.

Conclusion:
In projectile motion, the horizontal component of velocity is the only quantity that remains constant throughout the motion. The vertical component of velocity, the resultant velocity of projection, and the velocity of projection all change during the motion.