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.
at the beginning, till some time a,
h(t) = 200 - 16t^2
due to free-fall. When h(t) reaches 200 - max cord extension, the springy characteristics of the cord enter in. If the cord could rebound 100%, the wave would have a constant amplitude.
for t>a,
h(t) = b - c*cos(k(t-a))
which allows for an offset cosine wave, starting at its minimum.
However, the amplitude dampens exponentially, so the curve for t>a would more likely be something like
h(t) = b - c*cos(k1(t-a))*e^(-k2*(t-a))
So, a parabola to start with, then a damped cosine wave.
To sketch a reasonable graph of your distance above the water's surface as a function of time since you jumped, we can start by labeling the axes. Let's assume the x-axis represents time in seconds, and the y-axis represents your distance from the water's surface in feet.
Since you safely bungee jump from a 200-feet tall bridge, we should see a linear decrease in distance as time passes. This is because gravity is pulling you down towards the water's surface. Initially, you'll be at a height of 200 feet, and your distance will decrease until you reach the lowest point of the bungee jump.
Here's a rough sketch of the graph:
Distance (feet)
^
|
200 --+---------------------------------------
| |
| |
| |
| |
| |
|______________________________________> Time (seconds)
In this graph, the curve starts at a height of 200 feet and gradually decreases towards the lowest point of the bungee jump. The exact shape of the curve will depend on various factors, such as air resistance, the elasticity of the bungee cord, and the specific details of the jump.
To sketch a reasonable graph, we need to understand how the distance above the water's surface changes with time after bungee jumping from a 200-feet tall bridge.
Let's assume that at time 0 (the moment of jumping), you are at the top of the bridge, 200 feet above the water's surface. As time progresses, you will accelerate downwards due to the force of gravity.
As you fall, the speed at which you are descending will increase. However, once you reach the end of the bungee cord, it will start to stretch and eventually slow you down. This deceleration will continue until you reach the lowest point of your descent.
Subsequently, the bungee cord will contract and pull you back upwards. This upward movement will continue until the energy from the initial fall is dissipated, and you eventually come to a stop.
Based on this information, the graph will have the following shape:
1. At time 0, the graph will start at a height of 200 feet.
2. There will be a steep downward slope during the initial freefall as you accelerate under the force of gravity.
3. The graph will become less steep as the bungee cord stretches and slows your descent until you reach the lowest point.
4. After reaching the lowest point, there will be an upward slope as the bungee cord contracts, pulling you back up.
5. The graph will gradually flatten out until you come to a stop, indicating that the energy from the fall is dissipated.
It is important to note that the exact shape of the graph may vary depending on various factors such as the elasticity of the bungee cord, your weight, and the drag force acting on you during the fall.