Mechanics of practical situations

A student who is currently studying in class 11th11th 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 102m/s10\sqrt{2} m/s at an angle 450{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 PP. Then find P+0.5\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) =1.8×105Pa.s 1.8 \times {10}^{-5} Pa.s

3)Mass of the ball 3.3929g3.3929 g, Radius of the ball =1metre= 1 metre

3)Calculate percentage difference as :

TheorticalRangeObservedRangeTheorticalRange×100\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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