Question

In the projectile motion, if air resistance is ignored, the horizontal motion is at
A. Constant acceleration
B. Variable acceleration
C. Constant velocity
D. Constant retardation

Answer 1

We know that in projectile motion, due to gravity, there is a force acting in vertical downward direction at any given time. But, here we are asked to neglect the air resistance and therefore there is no force action in the horizontal direction. We will use this fact to determine the correct option regarding the horizontal motion.

Complete answer:
We know that if the air resistance is neglected in the projectile motion, the horizontal component of the force acting on the projectile at any given time will be zero, which means that ${F_x} = 0$.Now as per Newton’s second law of motion, force in the horizontal direction can be given as ${F_x} = m{a_x}$, where, $m$is the mass of the projectile and ${a_x}$is the acceleration in horizontal direction.
We have seen that
${F_x} = 0 \\\ \Rightarrow m{a_x} = 0 \\\ \Rightarrow {a_x} = 0$
Thus, there is no acceleration in horizontal direction.
As we know that acceleration is nothing but the rate of change of velocity with respect to time.Let us take ${v_x}$ as the velocity in horizontal direction.
$\dfrac{{d{v_x}}}{{dt}} = 0 \\\ \Rightarrow {v_x} = {\text{constant}}$
This means that if the derivative of horizontal velocity is zero, then the horizontal velocity does not change with time which means it is constant.Thus, in the projectile motion, if air resistance is ignored, the horizontal motion is at constant velocity.

Hence, option C is the right answer.

Note: Here, we have seen about the horizontal component of velocity. But if we consider the vertical component of velocity, in the projectile motion, according to the laws of motion, it is dependent on gravitational acceleration as the projectile experiences the gravitational force vertically and time. Thus, the vertical motion of the projectile will not be at constant velocity.