Question

A soccer ball is kicked off the ground with an initial vertical velocity of 28 feet per second. The height of the ball as a function of time can be modeled by the function h(t) = -16t^2 + 28t.

What is the maximum height reached by the soccer ball and how long will it take to get there?
A. 49 feet, 1 second
B. 56 feet, 2 seconds
C. 63 feet, 1.75 seconds
D. 70 feet, 3 seconds

Answer 1

The maximum height reached by the soccer ball is 49 feet, and it occurs at approximately 0.875 seconds, which corresponds to option A: 49 feet, 1 second when rounding to the nearest whole number and second.

Step-by-step explanation:

To determine the maximum height reached by the soccer ball and how long it will take to get there, we must find the vertex of the parabolic function h(t) = -16t2 + 28t that models the height of the ball as a function of time. The vertex of a parabola in the form of f(t) = at2 + bt + c can be found using the formula t = -b/(2a). In this case, a = -16 and b = 28, so the time at which the ball reaches its maximum height is t = -28/(2*(-16)) = 0.875 seconds.

Substituting t = 0.875 back into the function gives us h(0.875) = -16(0.875)2 + 28(0.875) = 49 feet. Therefore, the soccer ball reaches its maximum height of 49 feet after 0.875 seconds, which corresponds to option A: 49 feet, 1 second when rounded to the nearest whole number and second.