Final answer:
The graph for the sphere's horizontal velocity would be a flat line, as it remains constant in the absence of horizontal forces. The vertical velocity graph would show a deceleration while rising, hitting zero, and then an instantaneous change in direction due to the bounce. Vertical acceleration would be a constant negative value due to gravity.
Step-by-step explanation:
The scenario involves a sphere launched at a 45° angle bouncing off the ceiling, which follows the principles of projectile motion, commonly discussed in physics. We need to consider the characteristics of horizontal velocity and vertical velocity for the sphere as it moves through the air.
Horizontal velocity: Since there is no air resistance or other horizontal forces acting on the sphere, its horizontal component of velocity remains constant throughout the motion. Therefore, the graph of the sphere's horizontal velocity as a function of time would be a flat horizontal line.
Vertical velocity: The vertical component of velocity changes due to gravity's constant acceleration. At the moment of bounce on the ceiling, the direction of the velocity becomes the opposite, but the magnitude stays the same assuming an elastic and frictionless collision. Before the bounce, the graph would show a decreasing velocity (slowing down as it rises), reaching zero at the peak. After the bounce, there is an instantaneous change in the vertical velocity's direction indicated by a sharp vertical line on the graph.
Vertical acceleration: Because gravity is the only force acting vertically on the sphere, the vertical acceleration remains constant and negative (taking downward as negative). The graph of the ball's vertical acceleration versus time would be a horizontal line at the value of acceleration due to gravity, -9.81 m/s2.