The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of Find the angle rotated by the string before it becomes slack.

The angle reached before slack is

Given

The horizontal speed of the bob is

Formula Used

The formula for the total energy in terms of kinetic and potential energy is given as

where

The is the total energy in terms of kinetic and potential energy, m is the mass of the object, g is the acceleration in terms of gravity and l is the length of the object.

Explanation

The velocity at the lowest point is given as

The energy generated because of the potential and kinetic energy is calculated as

Replacing the length as

Hence, the angle reached before slack is