Chapter 1.2, Problem 35AYU

Motion οf a Golf Ball 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

$h\left(x\right)=\frac{-32x^2}{{130}^2}+x$

where $x$ is the horizontal distance that the golf ball has traveled.

(a) Determine the height of the golf ball after it has traveled 100 feet.

(c) What is the height after it has traveled 500 feet?

(d) How far was the golf ball hit?

(e) Use a graphing utility to graph the function $h=h(x)$.

(f) Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 90 feet.

(g) Create a TABLE with $TblStart=0$ and $\Delta Tbl=25$. To the nearest 25 feet, how far does the ball travel before it reaches a maximum height? What is the maximum height?

(h) Adjust the value of $\Delta Tbl$ until you determine the distance, to within 1 foot, that the ball travels before it reaches its maximum height.