A rope attaches a tire to an overhanging tree limb. A girl swinging on the tire has a centripetal acceleration of 3.0 m/s^2. If the length of the rope is 2.1 m, what is the girl's tangential speed?

centripetal acceleration= v^2/r

solve for v.

To find the girl's tangential speed, we can use the formula:

centripetal acceleration = (tangential speed)^2 / radius

Given data:
Centripetal acceleration = 3.0 m/s^2
Radius (length of the rope) = 2.1 m

Rearranging the formula to solve for tangential speed:

(tangential speed)^2 = centripetal acceleration * radius

tangential speed = √(centripetal acceleration * radius)

Plugging in the values:

tangential speed = √(3.0 m/s^2 * 2.1 m)

Calculating:

tangential speed ≈ √(6.3 m^2/s^2)

tangential speed ≈ 2.51 m/s

Therefore, the girl's tangential speed is approximately 2.51 m/s.