We are given the equation for the height of a golf ball:

$h(x) = \frac{-32x^2}{150^2} + x$

where:

• $h(x)$ is the height of the golf ball at a horizontal distance $x$,
• $x$ is the horizontal distance traveled.

Step 1: Plug $x = 350$ into the height function to find $h(350)$:

$h(350) = \frac{-32(350)^2}{150^2} + 350$

We can now calculate this value:

$h(350) = \frac{-32(122500)}{22500} + 350$ $h(350) = \frac{-3920000}{22500} + 350$ $h(350) = -174.22 + 350$ $h(350) = 175.78 \text{ feet}$

Step 2: Interpretation of the result

The value $h(350) = 175.78$ feet means that after the golf ball has traveled 350 feet horizontally, it is 175.78 feet above the ground.

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Would you like more details or clarifications?

Relative Questions:

1. How can we find the maximum height of the golf ball using calculus?
2. What is the horizontal distance when the golf ball hits the ground?
3. How does changing the initial velocity affect the height function?
4. How would the equation change if the angle of inclination were different?
5. How can we calculate the total time the ball spends in the air?

Tip:

When dealing with projectile motion problems, the angle and initial velocity greatly influence both the horizontal range and maximum height achieved by the object.