If a rock being swung on a rope experiences a centripetal acceleration of 40 m/s2
while traveling at 8 m/s, what is the length of the rope
v^2/r = 40
64/r = 40
r =64/40 =1.6 meters
but the rope slants down due to gravity
vertical acceleration = 9.8
in acceleration = 40
total = sqrt(40^2+9.8^2) = 41.2
L = 1.6 (41.2/40) = 1.65 meters