A golf ball is hit with an initial velocity of 150 feet per second at an inclination of \( 45^{\circ} \) to the horizontal. In physics, it is established that the height h of the golf ball is given by the function \[ \mathrm{h}(\mathrm{x})=\frac{-32 \mathrm{x}^{2}}{150^{2}}+\mathrm{x} \text {, } \] 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. \( \mathrm{h}=\square \) feet (Round to two decimal places as needed.)

To find the height of the golf ball after it has traveled 100 feet, we need to substitute the value of \( x = 100 \) into the given function \( h(x) = \frac{-32x^2}{150^2} + x \) and calculate the result. Given function: \( h(x) = \frac{-32x^2}{150^2} + x \) Substitute \( x = 100 \) into the function: \[ h(100) = \frac{-32(100)^2}{150^2} + 100 \] Now, let's calculate the height of the golf ball after it has traveled 100 feet. Calculate the value by following steps: - step0: Calculate: \(\frac{-32\times 100^{2}}{150^{2}}+100\) - step1: Reduce the fraction: \(-\frac{128}{3^{2}}+100\) - step2: Evaluate the power: \(-\frac{128}{9}+100\) - step3: Reduce fractions to a common denominator: \(-\frac{128}{9}+\frac{100\times 9}{9}\) - step4: Transform the expression: \(\frac{-128+100\times 9}{9}\) - step5: Multiply the numbers: \(\frac{-128+900}{9}\) - step6: Add the numbers: \(\frac{772}{9}\) The height of the golf ball after it has traveled 100 feet is approximately 85.78 feet.