9514 1404 393
Answer:
5.33 cm
Explanation:
The smallest positive zero of the polynomial with d=0.55 is about 5.33. We presume the units are cm.
The ball sinks to a depth of 5.33 cm.
__
I find a graphing calculator shows the zeros of higher-degree polynomials easily. The function graph is attached.
For the purpose here, the vertical scale factor π/3 can be eliminated, as it does not change the values of the zeros. That is, the polynomial we need to solve is x²(x -15) +275 = 0.
It turns out that a reasonable iterator for finding a solution is x' = √(275/(15 -x)). x = 5 is a reasonable starting point. The iterator is what you get by solving for the x outside the parentheses in the above cubic equation.