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 = 83.07 feet (round to two decimal places as needed.) (b) what is the height after it has traveled 300 feet? h = feet (round to two decimal places as needed.)

Explanation:

Step1: Identify the function

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

Step2: Substitute $x = 300$

Substitute $x = 300$ into the function: $h(300)=\frac{-32\times300^{2}}{140^{2}}+300$.
First, calculate $\frac{-32\times300^{2}}{140^{2}}=\frac{-32\times90000}{19600}=\frac{-2880000}{19600}\approx - 146.94$.
Then, $h(300)=-146.94 + 300$.

Step3: Calculate the result

$h(300)=153.06$ feet.

Answer:

$153.06$