Question

Which of the following statements are true of the horizontal motion of projectiles? List all that apply.a. A projectile does not have a horizontal velocity.b. A projectile with a rightward component of motion will have a rightward component of acceleration.c. The horizontal velocity of a projectile changes by 9.8 m/s each second.d. A projectile with a horizontal component of motion will have a constant horizontal velocity.e. The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory.f. The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other.g. The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity.h. The final horizontal velocity of a projectile is always equal to the initial horizontal velocity.i. As a projectile rises towards the peak of its trajectory, the horizontal velocity will decrease; as it falls from the peak of its trajectory, its horizontal velocity will decrease.

Answer 1

Answer:

d. A projectile with a horizontal component of motion will have a constant horizontal velocity.

f. The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other.

g. The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity.

h. The final horizontal velocity of a projectile is always equal to the initial horizontal velocity.

Explanation:

When we are dealing with parabolic motion, the x-component of the velocity remains the same (hence, in the case of the horizontal component, the acceleration will always be zero), while the y-component always change because it is affected by the acceleration due gravity that acts verticaly.

On the other hand, the horizontal displacement $x$ of the projectile is mathematically expressed as:

$x=V_{ox} t$  

Where:  

$V_{ox}$ is the projectile's horizontal component of the initial velocity  

$t$ is the time the parabolic motion lasts

This means the projectile's horizontal displacement is directly proportional to the horizontal component of the initial velocity and the total time the projectile describes the parabolic motion.

Of course, all of this considerations are assuming this is an ideal parabolic path and there is no air resistance.