Circular Motion Problem: Child swinging on a rope

[Mohammed S]

Homework Statement

A curious child finds a rope hanging vertically from the ceiling of a large storage hangar. The child grabs the rope and starts running in a circle. The length of the rope is 14.0m. When the child runs in a circle of radius 7.0m, the child is about to lose contact with the floor. How fast is the child running at that time?

Homework Equations

Fc=mv^2/r
a=v^2/r

The Attempt at a Solution

I tried finding the Fx of the length so 14cos(78.46)
I found the angle by doing SOH CAH TOA since the rope length and radius are in an angle
Anyways i heard v=radical rg but idk if its relevant
Then I got stuck

 

[gneill]

I found the angle by doing SOH CAH TOA since the rope length and radius are in an angle

Can you show us in detail how you found that angle? What angle is it?

I tried finding the Fx of the length so 14cos(78.46)

Did you draw a free body diagram (FBD) for the child? (can you show it to us?) What does "Fx of the length" mean?

What forces must be in balance for the child to just lose contact with the floor?

 

[Mohammed S]

Can you show us in detail how you found that angle? What angle is it?

Did you draw a free body diagram (FBD) for the child? (can you show it to us?) What does "Fx of the length" mean?

What forces must be in balance for the child to just lose contact with the floor?

So I attached an image of how to solve this, took me a while to solve but finally got it. Just plug in the values to find V and it's done! Thanks for helping tho!