HELP

Although your final value of 4.21m/s is correct GingerAle, you might want to check the values involved under the square root sign!

.

To solve this, use these two fundamental equations for pendulum motion.

$\text {F(net)}= 2T - m*g = m*a \hspace{1em} |\text {Force net,} \underbrace {\text{T is tension,}}_{\text {2 for the two chains}} \text {m is mass,}\\ \hspace{13em}\text { g is acceleration from gravity }(9.81 m/s^2), \\ \text { }\hspace{13em}\text {a is acceleration in the normal direction. } \\ $

$\text { And }\\ a = \dfrac {v^2}{ r} \hspace{1em} |\text { a is acceleration in the normal direction, v is the velocity,} \\ \hspace{4.7em} \text {r is the radius of the swing's arc. } \\$

$2T - m*g = m* (v^2 / r) \hspace{1em} | \text {solve for v } \\ \text { }\\ 2(441)- 53*9.81 = 53*\dfrac{v^2}{2.6}\\ \text { }\\ v = \sqrt{\dfrac{362.07}{53*2.6}}=4.21 m/s \hspace{1em} \Leftarrow \text {Solution}\\ $

-----------

Theory & Formulas: Complements of Christiaan Huygens, Galileo Galilei, and Sir Isaac Newton, et al. 

Produced by Lancelot Link and company.

Directed by GingerAle.

Sponsored by Naus Corp.

Thank you Sir Alan. Lancelot would throw banana peels at me for that.  

$v = \sqrt{\dfrac{362.07}{53}*2.6} = 4.21 m/s \hspace{1em} \Leftarrow \text {Solution -- }\textcolor {red} {(Corrected \;work \;product \;for \;solution.)}\\ $