Objects similar in size and shape will experience the similar dynamic fluid forces, but the more massive object will experience less acceleration.

$(25$ marks$)$

a$.$ Explain why it is easier to throw a curveball with a nerf ball than with a baseball or a tennis ball $($Fig$.1).$

b$.$ Given the mass of a baseball, tennis ball, and a nerf ball as $135$g$,45$g$,$ and $15$ g $,$ respectively, and the initial velocity for all as $50.$im$//$s $($where$,$ i$=|$i$\_(4)-$i$\_(5)|,$ i$.$e$.,$ the difference between the $4$th and $5$th digits of your Student ID counted from the left.$)$ with an angle $45$ degrees to the horizontal ground, how high and far can they travel if the air resistance is negligible?

c$.$ Supposing there is a $1\mathrm{.}5-$N backward drag force in the horizontal direction due to the air resistance, how far can they travel now?Please write all the solutions step by step in hand written.