A heavy ball is attached to a fixed point O by a light inextensible string of length 2a. The ball is drawn back until the string makes an acute angle α with the downward vertical and is then released from rest.
A thin peg is fixed a distance a vertically below O in the path of the string, as shown in given Figure. In a game of skill, the contestant chooses the value of α and wins a prize if the ball strikes the peg. Show that the winning value of α is approximately 86°.
