Question

The height of a football as a function of time is modeled by the function below where ( t ) is the number of seconds after the ball was kicked and ( h ) is the height in feet. After how many seconds is the ball 3 feet above the ground? Round to the nearest hundredth.

a. 0.33
b. 0.45
c. 0.51
d. 0.64

Answer 1

The football reaches a height of 3 feet at 0.54 seconds after being kicked, which is the smaller positive value given by the quadratic formula for this trajectory.

Step-by-step explanation:

The question revolves around the calculation of time when a football reaches a certain height after being kicked. Given that the use of the quadratic formula provides solutions for time t = 3.79 seconds and t = 0.54 seconds, and considering the context of the football's trajectory, we deduce that the ball reaches the height of 3 feet twice. First, as the ball goes up and then as it comes down.

For a situation like this, we typically take the smaller positive value, which would indicate when the ball passes the 3-foot height on its way up. Thus, the answer would be 0.54 seconds, which corresponds with answer option 'b.' Since the student is expected to round to the nearest hundredth, we confirm that 0.54 is indeed the correct answer already rounded to the nearest hundredth.