Final answer:
The graph of vertical velocity vs. time in projectile motion is a straight line that decreases to zero and then increases in the opposite direction. For a falling skydiver, the magnitude of velocity vs. time increases initially and then levels off at terminal velocity, while the magnitude of displacement vs. time shows a curve that becomes less steep as terminal velocity is reached.
Step-by-step explanation:
Graph of Vertical Velocity vs. Time in Projectile Motion
The graph of vertical velocity vs. time for an object in projectile motion, or in free fall, is a straight line. This is because the acceleration in the vertical direction (due to gravity) is constant. As the object is projected upwards, the vertical velocity decreases linearly with time due to the accelerating effect of gravity in the opposite direction. The highest point of the motion, where the vertical velocity is zero, is the peak of the trajectory. When the object descends, the vertical velocity increases linearly, but in the opposite direction, becoming negative if the upward direction is considered positive.
Graph of the Magnitude of Velocity vs. Time for a Falling Skydiver
For a falling skydiver, the graph of the magnitude of velocity vs. time initially increases as they accelerate due to gravity. However, as they reach terminal velocity, when the air resistance equals the gravitational force, the skydiver's velocity becomes constant and thus the graph levels off, indicating no further acceleration.
Graph of the Magnitude of Displacement vs. Time for a Falling Skydiver
The graph of the magnitude of displacement vs. time for a falling skydiver would show a curve representing increasing displacement with time. Initially, this curve would be steeper as the skydiver accelerates but would gradually become less steep as the skydiver reaches terminal velocity and moves downward at a constant speed.