Final answer:
Carlos's baseball follows a quadratic trajectory due to gravity, with key points including initial velocity, maximum height, time to peak, constant acceleration, and final velocity. Horizontal motion is absent if the ball is thrown straight up.
Step-by-step explanation:
When Carlos throws a baseball straight up into the air, the motion of the baseball is an example of vertical motion under the influence of gravity. The height the baseball reaches over time can be modeled by a quadratic function due to the constant acceleration due to gravity.
The path of the baseball would show it rising to a maximum height and then descending back down, which should be reflected in the provided graph. To answer the question about the ball's motion fully, consider the following key points:
The initial velocity can be calculated by looking at the height it reaches and the time it takes to reach that height.
The maximum height corresponds to the peak of the graph, where the vertical velocity of the ball is zero.
It takes half the total time in air for the ball to reach the maximum height, and the other half to descend to the catcher's hand.
The acceleration at the top of its path is due to gravity and is constant throughout the motion (around -9.81 m/s2).
The velocity of the ball when it is caught is equal in magnitude but opposite in direction to the initial velocity if air resistance is negligible.
In terms of the horizontal motion, assuming no air resistance and that Carlos threw the ball straight up, there would be no horizontal velocity or acceleration, so the graph of the ball's horizontal velocity would be a horizontal line at zero.
Vertical Motion of a Baseball Example
Referring to the example given, where a baseball is hit straight upward and caught 5 seconds after, the calculations would involve the equations of motion under constant acceleration. Equation 4.22 could be used to find the time it takes for the ball to rise and fall to its final position. The vertical motion can be analyzed separately from the horizontal motion for a projectile in two-dimensional motion.