Agirl on swing varies height from 60cm above the ground to 180cm. what is girls greatest velocity?

At highest point, velocity = 0, height (potential energy) is max 
at lowest point, velocity(Kinetic energy) is max, height (PE) is reduced

total energy at 2 points is equal --- conservation of energy. in the other words, potential energy transform to kinetic energy when decending. 

PE reduce = KE increase 
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mg(180) - mg(60) = 0.5mv^2 - 0 
g(180-60) = 0.5v^2 
work from here 
... remark ... unit of v is cm/s

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