the \hang time\ of a football is the amount of time the football stays in the air after being kicked. zara…
the \hang time\ of a football is the amount of time the football stays in the air after being kicked. zara kicks a football, and the height (in meters) of the football above the ground at t seconds is shown in the graph below. complete the following sentences based on the graph of the function. · this is the graph of a function. · the hang time of the football is second(s). · the football reaches its maximum height when t = second(s). · the maximum height is about meter(s). (round your answer to the nearest whole meter.) · for t between t = 0 and t = 1.5, the height is.
Answer
Explanation:
Step1: Identify function type
Since for each value of (t) (input - time), there is exactly one value of (h) (output - height), it is a one - to - one function. In the context of height over time for a projectile, it is a quadratic function (a parabola opening downwards).
Step2: Find hang time
The hang time is the time when the football hits the ground again. Looking at the graph, if the graph starts at (t = 0) and touches the (t) - axis again at (t=3), the hang time is 3 seconds.
Step3: Find time of maximum height
The maximum of a parabola occurs at its vertex. By observing the graph, the (t) - value at the vertex is (t = 1.5) seconds.
Step4: Find maximum height
By looking at the (h) - value at (t = 1.5) on the graph, the maximum height is about 11 meters.
Step5: Analyze height change
For (t) between (t = 0) and (t=1.5), as (t) increases, the height (h) of the football is increasing.
Answer:
- This is the graph of a quadratic function.
- The hang time of the football is 3 second(s).
- The football reaches its maximum height when (t = 1.5) second(s).
- The maximum height is about 11 meter(s).
- For (t) between (t = 0) and (t = 1.5), the height is increasing.