Calculating Tarzan's Max Swing Speed

[Quantum Fizzics]

Homework Statement

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting a force of 1500N on the rope, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 85kg; the vine is 4.0m long

Homework Equations

Fc = mv2/r
Fg = mg
T = Fc +Fg
Fc = T-Fg

The Attempt at a Solution

How I did it at first was:
T = Fc+ Fg
Fc=T-Fg
mv^2/r = 1500 -mg
V^2/4 =1500 - 10(cancelled out the masses)
v = 1500 -10(4) ~~~~(idk how to the square root in my calculator hopefully u get the idea)
v = 38.2 m/s
-----------------------------
The answer was wrong according to the textbook( 5.6m/s at the lowest point of the swing)
So I tried another way starting from the side
T = Fc
1500 = mv^2/r
1500 = 85v^2/4
1500(4)/85 (square root) = v
v= 1.823 m/s
-------------------------
WHAT HAVE I DONE WRONG :c I used the equations I was taught but meeh please help

 

[SteamKing]

Homework Statement

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting a force of 1500N on the rope, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 85kg; the vine is 4.0m long

Homework Equations

Fc = mv2/r
Fg = mg
T = Fc +Fg
Fc = T-Fg

The Attempt at a Solution

How I did it at first was:
T = Fc+ Fg
Fc=T-Fg
mv^2/r = 1500 -mg
V^2/4 =1500 - 10(cancelled out the masses)

How do you cancel out the masses and leave the 1500 unchanged? This is where your problems start.

v = 1500 -10(4) ~~~~(idk how to the square root in my calculator hopefully u get the idea)
v = 38.2 m/s
-----------------------------
The answer was wrong according to the textbook( 5.6m/s at the lowest point of the swing)
So I tried another way starting from the side
T = Fc
1500 = mv^2/r
1500 = 85v^2/4
1500(4)/85 (square root) = v
v= 1.823 m/s
-------------------------
WHAT HAVE I DONE WRONG :c I used the equations I was taught but meeh please help

It takes more than just memorizing some equations. You've got to get the math right as well.