Mechanics of practical situations

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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