$textbf{Solution:}$ From definition of impulse.

$$
I=Delta t
$$

$$
Rightarrow F=frac{I}{Delta t}=frac{23,kg.m/s}{0.25,s}
$$

$$
boxed{bf color{#4257b2}I=92,N}
$$

The mass of the two apples is equal $m_{1} = m_{2} = m$. The displacement that the apple $1$ takes is $Delta x_{1} = 2 mathrm{~m}$. The displacement that the apple $2$ takes is $Delta x_{2} = 3 mathrm{~m}$.

$textbf{Required: }$

Compare between the impulse of the two apples with explanation.

Solve for the apple $1$:

In order to evaluate the displacement that the apple takes, we use the following relation:

$$
begin{align*}
Delta x_{1} &= v_{i} ~ t_{1} + dfrac{1}{2} ~ g ~ t_{1}^{2} \
&= 0 +dfrac{1}{2} ~ g ~ t_{1}^{2} \
&= dfrac{1}{2} ~ g ~ t_{1}^{2}
end{align*}
$$

Rearrange and solve for the time interval $t_{1}$:

$$
begin{align*}
t_{1} &= sqrt{ dfrac{ 2 ~Delta x_{1} }{ g} } \
&= sqrt{ dfrac{ 2 times 2 mathrm{~m} }{ g} } \
&= 2 ~ sqrt{ dfrac{m}{g} }\
end{align*}
$$

As the textbook assigns that the impulse is the product of a force and the time which is given by

$$
begin{align*}
vec{I_{1}} &= vec{F_{1}} ~ t_{1} \
&= m_{1} ~ g ~ t_{1} \
&= m ~ g ~ 2 ~ sqrt{ dfrac{m}{g} }\
&= 2 ~ sqrt{m^{3} ~ g } \
end{align*}
$$

Solve for the apple $2$:

In order to evaluate the displacement that the apple $2$ takes, we use the following relation:

$$
begin{align*}
Delta x_{2} &= v_{i} ~ t_{2} + dfrac{1}{2} ~ g ~ t_{2}^{2} \
&= 0 +dfrac{1}{2} ~ g ~ t_{2}^{2} \
&= dfrac{1}{2} ~ g ~ t_{2}^{2}
end{align*}
$$

Rearrange and solve for the time interval $t_{1}$:

$$
begin{align*}
t_{2} &= sqrt{ dfrac{ 2 ~Delta x_{2} }{ g} } \
&= sqrt{ dfrac{ 2 times 3 mathrm{~m} }{ g} } \
&= sqrt{ dfrac{6m}{g} }\
end{align*}
$$

As the textbook assigns that the impulse is the product of a force and the time which is given by

$$
begin{align*}
vec{I_{2}} &= vec{F_{2}} ~ t_{2} \
&= m_{2} ~ g ~ t_{2} \
&= m ~ g ~ sqrt{ dfrac{6m}{g} }\
&= sqrt{6m^{3} ~ g } \
&= 2.449 ~ sqrt{m^{3} ~ g } \
end{align*}
$$

So, the impulse delivered by gravity to apple $1$ is less than the impulse delivered by gravity to apple $2$.