Question

1. you (safely) bungee jump from a 200-feet tall bridge in your town. your distance above the waters surface depends on the time since you jumped. sketch a reasonable graph. (3 points)

Explanation:

1. Axes Setup: The horizontal axis represents time ($t$, in seconds) and the vertical axis represents distance above water ($d$, in feet).
2. Initial State: At $t=0$, the starting height is 200 feet, so the graph starts at the point $(0, 200)$.
3. First Fall: The distance decreases rapidly and linearly at first (free fall before the bungee cord tightens) until reaching the lowest point, where the distance is at its minimum (greater than 0, since the jump is safe).
4. Bounce Cycle: After the first low point, the cord recoils, pulling the jumper upward, so the distance increases. This is followed by another downward fall (distance decreases) but to a lower maximum height and higher minimum distance than the first cycle, due to energy loss from the cord and air resistance.
5. Stabilization: Over time, the bounces get smaller (amplitude decreases) until the jumper comes to rest at a constant distance above the water (the graph levels off to a horizontal line at the equilibrium height of the bungee cord and jumper).

Answer:

A reasonable graph has:

• A horizontal time axis and vertical distance axis.
• Starts at $(0, 200)$.
• Decreases steeply to a first minimum distance > 0.
• Oscillates (up and down curves) with decreasing height of peaks and increasing height of troughs.
• Levels off to a horizontal line at a constant equilibrium distance above the water.