a cyclist rides at a constant speed of 4.5 m/s around a curve. if the centripetal acceleration is 29 m/s²…

Explanation:

Step1: Recall centripetal - acceleration formula

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$, where $a_c$ is centripetal acceleration, $v$ is speed, and $r$ is the radius of the curve. We need to solve for $r$.

Step2: Rearrange the formula for $r$

Rearranging $a_c = \frac{v^{2}}{r}$ gives $r=\frac{v^{2}}{a_c}$.

Step3: Substitute given values

We are given that $v = 4.5$ m/s and $a_c=29$ m/s². Substituting these values into the formula $r=\frac{v^{2}}{a_c}$, we get $r=\frac{(4.5)^{2}}{29}=\frac{20.25}{29}\approx0.70$ m.

Answer:

0.70 m