Answer:
a = 12.8 m/s^2
Explanation:
To find the centripetal acceleration you use the following formula:
[tex]a_c=\frac{v^2}{r}[/tex] (1)
v: tangential speed of the rock = 17.90mph
r: radius of the orbit = 1000cm/2 = 500cm = 0.5m
You first change the units of the tangential velocity in order to replace the values of v and r in the equation (1):
[tex]17.90mph*\frac{1609.34m}{1\ m}*\frac{1\ h}{3600\ s}=8m/s[/tex]
Then, you use the equation (1):
[tex]a_c=\frac{(8m/s)^2}{5m}=12.8\frac{m}{s^2}[/tex]
hence, the centripetal acceleration is 12.8 m/s^2
