Question

The following table shows the number of feet a helicopter flies above the ground as a function of time: Time (in seconds) x Distance above ground (in feet) f(x) 0 18 2 16 4 14 6 12 8 10 Find and interpret the meaning of the x-intercept in this scenario. (10, 0); the time it takes for the helicopter to reach the ground (18, 0); the time it takes the helicopter to take off (10, 0); the time it takes the helicopter to take off (18, 0); the time it takes for the helicopter to reach the ground

Answer 1

The x-intercept of a position vs. time graph represents the time at which the position becomes zero. In the helicopter scenario, the x-intercept (10, 0) signifies that it takes 10 seconds for the helicopter to reach the ground from an initial altitude of 18 feet.

Step-by-step explanation:

The x-intercept in a position vs. time graph represents the point where the position of the object is zero. Looking at the table you've provided, if we see the position decreasing over time, we can assume a constant decrease in altitude. Therefore, when we extend this data to find the x-intercept, we are looking for the point in time where the helicopter reaches the ground, meaning that its altitude or distance above the ground is zero.

Since the helicopter is losing 2 feet for every second (as we can tell from the rate of decrease in altitude from the table: 18, 16, 14, 12, 10), it will take 5 more seconds from the last data point (at 8 seconds, 10 feet) to reach the ground. Thus, after 10 seconds in total, the helicopter will be at 0 feet above the ground. This interprets the x-intercept (10, 0) as the time it takes for the helicopter to reach the ground, which aligns with the physical scenario of a helicopter making a landing.