Question

a golf ball is hit with an initial velocity of 130 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}}{130^{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 = 81.07 feet (round to two decimal places as needed.) (b) what is the height after it has traveled 250 feet? h = feet (round to two decimal places as needed.)

Explanation:

Step1: Substitute x = 250 into the height - function

Given \(h(x)=\frac{-32x^{2}}{130^{2}}+x\), substitute \(x = 250\). First, calculate \(\frac{-32x^{2}}{130^{2}}\) when \(x = 250\).
\(\frac{-32\times250^{2}}{130^{2}}=\frac{-32\times62500}{16900}=\frac{-2000000}{16900}\approx - 118.3432\)

Step2: Calculate the value of \(h(250)\)

\(h(250)=\frac{-32\times250^{2}}{130^{2}}+250\approx - 118.3432 + 250\)
\(h(250)\approx131.66\)

Answer:

131.66