In a region, potential energy varies with X as `U(x)=30-(x-5)^(2)` Joule, where x is in meters. A particle of mass 0.5 kg is projected from x=11 m towards origin with a velocity 'u' . u is the minimum velocity, so that the particle can reach the origin. (x=0). find the value of u/2 in meter/second. (Take `sqrt(44)=6.5`)

Explanation

To solve the problem, we need to determine the minimum velocity \( u \) required for a particle of mass \( 0.5 \, \text{kg} \) to reach the origin (x = 0) when projected from \( x = 11 \, \text{m} \). The potential energy \( U(x) \) is given by:

\[ U(x) = 30 - (x - 5)^2 \, \text{J} \]

### Step 1: Determine the potential energy at the initial position (x = 11 m)

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