A particle is suspended from a fixed point by a string of lengh `5m`. It is projected from the equilibrium position with such a velocity that the string slakens after the particle has reached a height `8m` above lowest point. Find the velocity of the particle, just before the string slackens.
Find also, to what to what height the particle can rise further?

Explanation

To solve the problem step by step, we will use the principles of circular motion and projectile motion.

### Step 1: Understanding the Problem
We have a particle suspended by a string of length 5 m. The particle is projected from the equilibrium position and reaches a height of 8 m above the lowest point before the string slackens. We need to find the velocity of the particle just before the string slackens and the maximum height it can reach after that.

### Step 2: Determine the Effective Length of the String
When the particle reaches a height of 8 m, the vertical distance from the lowest point to the particle is 8 m. The length of the string is 5 m, so the distance from the point where the string is attached to the particle is given by:

...