Final answer:
The shape of the graph of horizontal velocity vs. time in projectile motion is a horizontal line, reflecting that the horizontal velocity remains constant over time when air resistance is ignored.
Step-by-step explanation:
The graph of horizontal velocity vs. time in projectile motion is a horizontal line, indicating that the horizontal velocity (βx) remains constant throughout the motion, assuming no air resistance. Because the horizontal acceleration (βx) is zero, there is no change in horizontal velocity as the projectile moves. This means that the horizontal component of the projectile's motion does not change as time progresses, which is distinct from the vertical component of the projectile's motion where the vertical velocity changes due to the acceleration caused by gravity.
In projectile motion, the horizontal velocity of the projectile remains constant throughout its flight (assuming no air resistance). Therefore, the graph of horizontal velocity vs. time is a horizontal line. The slope of this line represents the constant horizontal velocity, indicating that the projectile moves with a consistent speed in the horizontal direction.
If you were to plot this graph, the x-axis would represent time, and the y-axis would represent horizontal velocity. The resulting graph would be a straight line parallel to the time axis, indicating that the horizontal velocity does not change over time during the projectile motion. This is a characteristic feature of projectile motion under ideal conditions.