Question

A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 30 m. if he completes the 200 m dash in 20.4 s and runs at constant speed throughout the race, what is his centripetal acceleration as he runs the curved portion of the track in m/s²?

Answer 1

The centripetal acceleration of the runner as they run the curved portion of the track is 2.47 m/s².

Step-by-step explanation:

The centripetal acceleration of a runner as they run the curved portion of the track can be calculated using the formula:

ac = v^2 / r

Where ac is the centripetal acceleration, v is the runner's constant speed, and r is the radius of curvature of the track. In this case, the runner completes the 200 m dash in 23.2 s, so the runner's speed is v = 200 m / 23.2 s = 8.62 m/s. The radius of curvature is 30 m. Plugging these values into the formula, we have:

ac = (8.62 m/s)^2 / 30 m = 2.47 m/s²