MATH SOLVE

4 months ago

Q:
# A typical running track is an oval with 74-m-diameter half circles at each end. a runner going once around the track covers a distance of 400 m . suppose a runner, moving at a constant speed, goes once around the track in 1 min 40 s. what is her centripetal acceleration during the turn at each end of the track?

Accepted Solution

A:

Answer:Her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]Step-by-step explanation:Total distance covered in one round , D= 400 mTime taken to cover one round , T = 1 min 40 s = 100 secSpeed of runner , [tex]V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}[/tex]Now centripetal acceleration is given by[tex]a_c=\frac{V^{2}}{R}[/tex]where [tex]V= 4.0\frac{m}{s}[/tex][tex]Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m[/tex][tex]\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}[/tex]Thus her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]