Estimate the maximum speed with which you could take the curve in Example 11.4.

Data from Example 11.4

A woman is rollerblading to work and, running late, rounds a corner at full speed, sharply leaning into the curve (Figure 11.25). If, during the turn, she goes along the arc of a circle of radius \(4.5 \mathrm{~m}\) at a constant speed of \(5.0 \mathrm{~m} / \mathrm{s}\), what angle \(\theta\) must her body make with the vertical in order to round the curve without falling?

Figure 11.25 Example 11.4.