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 (c)
(a) determine the height of the golf ball after it has traveled 100 feet
(h = 83.67) feet (round to two decimal places as needed.)
(b) what is the height after it has traveled 300 feet?
(h = 153.06) feet (round to two decimal places as needed.)
(c) what is (h(400))? interpret this value.
(h(400)=136.73) 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 (square) feet
b. at a height of 400 feet, the horizontal distance traveled by the golf ball is (square) feet

Question

Accepted Answer

# Explanation:
## Step1: Identify the height - function
The height function of the golf - ball is $h(x)=\frac{-32x^{2}}{140^{2}}+x$, where $x$ is the horizontal distance.
## Step2: Calculate the height when $x = 100$
Substitute $x = 100$ into the function:
$$
\begin{align*}
h(100)&=\frac{-32\times100^{2}}{140^{2}}+100\
&=\frac{-32\times10000}{19600}+100\
&=\frac{-320000}{19600}+100\
&=-\frac{800}{49}+100\
&=\frac{-800 + 4900}{49}\
&=\frac{4100}{49}\approx83.67
\end{align*}
$$
## Step3: Calculate the height when $x = 300$
Substitute $x = 300$ into the function:
$$
\begin{align*}
h(300)&=\frac{-32\times300^{2}}{140^{2}}+300\
&=\frac{-32\times90000}{19600}+300\
&=\frac{-2880000}{19600}+300\
&=-\frac{7200}{49}+300\
&=\frac{-7200+14700}{49}\
&=\frac{7500}{49}\approx153.06
\end{align*}
$$
## Step4: Calculate $h(400)$ and interpret
Substitute $x = 400$ into the function:
$$
\begin{align*}
h(400)&=\frac{-32\times400^{2}}{140^{2}}+400\
&=\frac{-32\times160000}{19600}+400\
&=\frac{-5120000}{19600}+400\
&=-\frac{12800}{49}+400\
&=\frac{-12800 + 19600}{49}\
&=\frac{6800}{49}\approx138.78
\end{align*}
$$
The value $h(400)$ represents the height of the golf - ball after it has traveled a horizontal distance of 400 feet. The correct interpretation is: The height of the golf ball after it has traveled a horizontal distance of 400 feet is 138.78 feet.

# Answer:
(a) $h\approx83.67$ feet
(b) $h\approx153.06$ feet
(c) $h(400)\approx138.78$ feet; The height of the golf ball after it has traveled a horizontal distance of 400 feet is 138.78 feet.

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the height - function

Step2: Calculate the height when $x = 100$

Step3: Calculate the height when $x = 300$

Step4: Calculate $h(400)$ and interpret

Answer: