Answer:
[tex]a=8.5m/s^2[/tex]
Explanation:
The total acceleration will be the vectorial sum of the tangential and centripetal accelerations, since they would be the only ones acting on Cheryl. They are perpendicular to each other, so the magnitude of the sum is given by:[tex]a=\sqrt{a_{t}^2+a_{cp}^2}[/tex]
Since the centripetal acceleration is given by the formula [tex]a_{cp}=\frac{v^2}{r}[/tex], we have:
[tex]a=\sqrt{a_{t}^2+(\frac{v^2}{r})^2}[/tex]
Which for our values is:
[tex]a=\sqrt{(3m/s^2)^2+(\frac{(4m/s)^2}{(2m)})^2}=8.5m/s^2[/tex]
