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

Explanation:

Step1: Identify the function and value of x

The function is $h(x)=\frac{- 32x^{2}}{140^{2}}+x$, and $x = 100$.

Step2: Substitute x into the function

$h(100)=\frac{-32\times100^{2}}{140^{2}}+100$.
First, calculate $\frac{-32\times100^{2}}{140^{2}}=\frac{-32\times10000}{19600}=\frac{-320000}{19600}\approx - 16.33$.
Then, $h(100)=-16.33 + 100$.

Step3: Calculate the final result

$h(100)=83.67$.

Answer:

$83.67$