A student who is currently studying in class \(11th\) gets excited to learn about projectiles and decides to test one out himself. He buys a ball throwing cannon for this purpose whose angle and velocity can be adjusted accordingly. He throws the projectile from a point on the ground at a velocity \(10\sqrt{2} m/s\) at an angle \({45}^{0}\).

He expects that he would get the exact range but the observed range is somewhat different. Let the percentage difference in the range of the projectile be \(P\). Then find \(\lfloor P+0.5 \rfloor \)

**Details and Assumptions**

1)Consider only stokes drag, no newtonian drag.

2)Co-efficient of viscosity of air(Dynamic Viscosity) =\( 1.8 \times {10}^{-5} Pa.s \)

3)Mass of the ball \(3.3929 g\), Radius of the ball \(= 1 metre\)

3)Calculate percentage difference as :

\(\frac{Theortical Range - Observed Range}{TheorticalRange} \times 100 \)

4)Range is calculated as the distance between the points when the centre of sphere were at the same point when it touched the ground. See diagram.

5)Neglect buoyancy.

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