Grigoriy S. answered 12/04/21
AP Physics / Math Expert Teacher With 40 Years of Proven Success
To solve the problem, you need to use the law of conservation of mechanical energy. On the bottom the monkey has only kinetic energy K = 1/2 mv2. Then it moves up and all kinetic energy will be converted to potential energy of the pendulum U = mgh, here h - height against zero's level of energy. In this case it is the line, that is parallel to the surface and going through bottom point. You can write
mgh = 1/2 mv2
From this equation you will get expression for height
h = v2 /2g