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 7 s have elapsed?
35.5s
To determine the height of the helicopter after 7 seconds have elapsed, we need to find the area under the graph of its vertical velocity as a function of time. The area under a velocity-time graph represents the displacement or distance traveled.
Looking at the graph, we see that the vertical velocity of the helicopter increases steadily from 0 m/s to 30 m/s over the course of 7 seconds. Therefore, we can treat the graph as a trapezoid.
First, let's calculate the area of the trapezoid. The formula for the area of a trapezoid is:
Area = (base1 + base2) * height / 2
In this case, one base is 0 m/s (at t = 0) and the other base is 30 m/s (at t = 7). The height of the trapezoid is 7 seconds.
Area = (0 m/s + 30 m/s) * 7 s / 2 = 15 m/s * 7 s / 2 = 52.5 m
Thus, the area under the graph, which represents the displacement or distance traveled by the helicopter, is 52.5 meters.
Therefore, the helicopter is approximately 52.5 meters high after 7 seconds have elapsed.