# Projectile + Vertical Circle = Double Trouble

**Classical Mechanics**Level 4

A heavy particle is suspended by a string of length \(L\) from a fixed point \(O\). The particle is given a horizontal velocity \(v\). The string slacks at some angle and particle proceeds on a projectile path. The particle proceeds such that after becoming a projectile it passes through the point of suspension.

If the value of \(v^2\) can be expressed as \( v^2 = gL \ \tan(x) \), for positive acute angle \(x\) then find the measure of \(x\) in degrees.

**Details And Assumptions**:

Take acceleration due to gravity to be constant \(10 \text{ m/sec}^2 \).

The initial motion of the particle (that is before becoming a projectile) is motion along a vertical circle (motion is in vertical plane).

At the instant of slacking the tension in the string will become zero.

The string is light and inextensible.

Neglect air resistance and consider the particle to be a point mass.