1. You (safely) bungee jump from a 200-feet tall bridge in your town. Your distance above the water's surface depends on the time since you jumped. Sketch a reasonable graph.
To sketch a reasonable graph representing the scenario, we need to understand how the distance above the water's surface changes over time while bungee jumping.
When you bungee jump, your initial distance above the water's surface is 200 feet. As time passes, you start falling downward due to gravity. However, as the bungee cord stretches and begins to exert an upward force, your descent slows down and eventually stops. Then, the cord begins to contract, pulling you back upward.
The graph will have a distinct shape that reflects these changes. Initially, the graph will show a steep downward slope representing a rapid descent. As the bungee cord stretches, the graph will flatten out, indicating a decreasing rate of descent. At the point of maximum stretch, the graph will have a horizontal line representing zero velocity, indicating the momentary stop in your descent. Finally, as the bungee cord contracts, the graph will slope upwards again, representing the ascent back above the water's surface.
The specific shape of the graph will depend on various factors such as the elasticity of the bungee cord and the damping forces involved. Nonetheless, a general sketch of the graph would have a steep downward slope followed by a flatter section, then a horizontal line, and finally an upward slope.
Keep in mind that safety is of utmost importance when bungee jumping. Always consult professionals, follow guidelines, and ensure proper equipment and procedures are in place.