A helicopter is lifting off from the ground and is moving vertically upward. The graph shows its vertical velocity vy versus time. How high is the helicopter after 12.0 s have elapsed?
Are you supposed to be reading the graph?
101
To determine the height of the helicopter after 12.0 seconds have elapsed, we first need to understand the information given in the graph. The graph represents the vertical velocity (vy) of the helicopter as a function of time.
Since the helicopter is moving vertically upward, the positive values of vy represent the upward direction, while the negative values represent the downward direction.
To find the height, we need to integrate the vertical velocity function over the given time interval. Integration is used to find the displacement or change in height.
Since the vertical velocity function gives us the rate of change of height, integrating it would give us the total change in height.
To integrate the graph, we need to find the area under the curve between the initial time (t = 0) and the given time (t = 12.0 s).
Here are the steps to calculate the height:
1. Identify the region under the curve on the graph corresponding to the time interval from t = 0 to t = 12.0 s.
2. Calculate the area under the curve within this time interval. The area gives us the change in height.
3. Calculate the definite integral of the vertical velocity function between t = 0 and t = 12.0 s. This will give us the displacement or height change over the given time interval.
4. The integral will provide the height change, but we still need to determine the initial height. If the initial height is not given, you can assume it to be zero.
5. Add the initial height to the height change to get the total height after 12.0 seconds.
Please note that to perform the integral and obtain a numerical value, you need the functional form of the vertical velocity function. If you provide the function, we can assist you further in calculating the height.