Question

a golf ball is hit with an initial velocity of 140 feet per second at an inclination of 45° to the horizontal. in physics, it is established that the height h of the golf ball is given by the function h(x)=\frac{-32x^{2}}{140^{2}}+x, where x is the horizontal distance that the golf ball has traveled. complete parts (a) through (g). (b) what is the height after it has traveled 260 feet? h = 147.96 feet (round to two decimal places as needed.) (c) what is h(400)? interpret this value. h(400)=138.78 feet (round to two decimal places as needed.) interpret the value of h(400). choose the correct answer below and fill in the answer box to complete your choice. a. the height of the golf ball after it has traveled a horizontal distance of 400 feet is 138.78 feet. b. at a height of 400 feet, the horizontal distance traveled by the golf ball is feet. (f) how far was the golf ball hit? x = feet (round to two decimal places as needed.)

Explanation:

Step1: Recall the height - function

The height function of the golf - ball is $h(x)=\frac{- 32x^{2}}{140^{2}}+x$.

Step2: Find the maximum of the quadratic function

For a quadratic function $y = ax^{2}+bx + c$ ($a
eq0$), the x - coordinate of the vertex (which gives the maximum for $a\lt0$) is $x=-\frac{b}{2a}$. In our function $h(x)=\frac{-32}{140^{2}}x^{2}+x$, where $a = \frac{-32}{140^{2}}$ and $b = 1$.
First, calculate $x=-\frac{b}{2a}=-\frac{1}{2\times\frac{-32}{140^{2}}}=\frac{140^{2}}{64}$.
$140^{2}=19600$, so $x=\frac{19600}{64}=306.25$ feet.

Answer:

$306.25$