To model the height of the golf ball as a function of its distance from Lynn, we can use a quadratic equation in the form of:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola. In your scenario, the highest point of the ball is 30 feet at a distance of 60 feet from Lynn. Thus, the vertex is (60, 30).
Since the ball lands 60 feet away from her, we can assume that it is symmetrical, meaning it starts from the ground level (height = 0) at x = 0 feet and reaches back to ground level at x = 60 feet.
- The vertex (h, k) is (60, 30).
- The function must pass through the points (0, 0) and (60, 0).
We can find the value of 'a' by using one of the points. Using the vertex form:
f(0) = a(0 - 60)² + 30 = 0.
This simplifies to:
0 = a(3600) + 30 -30 = 3600a a = -30/3600 a = -1/120.
Now we can write the equation as follows:
f(x) = -1/120(x - 60)² + 30.
To find the height when the ball is 15 feet away from Lynn (x = 15):
f(15) = -1/120(15 - 60)² + 30 = -1/120(-45)² + 30 = -1/120(2025) + 30 = -2025/120 + 30 = -17.1875 + 30 = 12.8125.
Now, writing 12.8125 as a fraction, we can express it as:
12.8125 = 12 + 0.8125 = 12 + 13/16 = 12 13/16.
Thus:
The ball when it is 15 feet from Lynn is 12 13/16 feet.
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