Math Snap

STEP 1

Assumptions1. The initial velocity of the golf ball is130 feet per second.
. The golf ball is hit at an angle of $45^{\circ}$ to the horizontal.
3. The height $h$ of the golf ball is given by the function $$h(x)=\frac{-32 x^{}}{130^{}}+x$$ where $x$ is the horizontal distance that the golf ball has traveled.

STEP 2

To find the height of the golf ball after it has traveled100 feet, we need to substitute $x =100$ into the given function.
$$h(100)=\frac{-32 \times100^{2}}{130^{2}}+100$$

STEP 3

First, calculate the square of100.
$$100^{2} =10000$$

STEP 4

Substitute $100^{2}$ into the equation.
$$h(100)=\frac{-32 \times10000}{130^{2}}+100$$

STEP 5

Calculate the product of -32 and10000.
$$-32 \times10000 = -320000$$

STEP 6

Substitute $-32 \times10000$ into the equation.
$$h(100)=\frac{-320000}{130^{2}}+100$$

STEP 7

Next, calculate the square of130.
$$130^{2} =16900$$

STEP 8

Substitute $130^{2}$ into the equation.
$$h(100)=\frac{-320000}{16900}+100$$

STEP 9

Calculate the division of -320000 by16900.
$$\frac{-320000}{16900} \approx -18.93$$

STEP 10

Substitute $\frac{-320000}{16900}$ into the equation.
$$h(100)=-18.93+100$$

Calculate the sum of -18.93 and100.
$$-18.93+100 =81.07$$The height of the golf ball after it has traveled100 feet is approximately81.07 feet.