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). (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)=square feet (round to two decimal places as needed.)

Explanation:

Step1: Identify the height - function

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

Step2: Substitute $x = 400$ into the function

We substitute $x = 400$ into $h(x)$. First, calculate $\frac{-32\times400^{2}}{140^{2}}$:
$\frac{-32\times400^{2}}{140^{2}}=\frac{-32\times160000}{19600}=\frac{-5120000}{19600}\approx - 261.22$.
Then, $h(400)=\frac{-32\times400^{2}}{140^{2}}+400$.
$h(400)\approx - 261.22 + 400$.

Step3: Calculate the result

$h(400)=138.78$

Answer:

$138.78$