91Ó°ÊÓ

The given data can be listed below as,

The drag force which is also known as air resistance, it is the force that act on an object opposite to its relative motion while object is moving in air.

Part (a)

The expression for drag force according to Newton’s second law when ball is moving up can be expressed as,

$∑F_y=f+w$

Here$f$is drag force, is the weight.

Substitute $ma$for ,$F_y$and$\frac{1}{4}mg$for $f$, and $mg$for$w$in the above equation.

$\begin{array}{c}ma=\frac{1}{4}mg+mg\\ ma=\frac{5}{4}mg\\ a=\frac{5}{4}g\end{array}$

Hence, required acceleration of ball when it is moving up is, .$\frac{5}{4}g$

Part (b)

The expression for drag force according to Newton’s second law when ball is moving back down can be expressed as,

$∑F_y=w−f$

Substitute $ma$for $F_y$, and $\frac{1}{4}mg$for $f$, and $mg$for $w$in the above equation.

$\begin{array}{c}ma=mg−\frac{1}{4}mg\\ ma=\frac{3}{4}mg\\ a=\frac{3}{4}g\end{array}$

Hence, required acceleration of ball when it is moving back down is,$\frac{3}{4}g$ .