While taking a shower, you notice that the shower head is made up of $48$ small round openings, each with a radius of $2\mathrm{.}00$ mm $.$ You also determine that it takes $4\mathrm{.}00$ s for the shower to completely fill a $1\mathrm{.}00-$liter container you hold in the water stream. The water for the shower is pumped by a pump that is $5\mathrm{.}60$ m below the level of the shower head. The pump maintains an absolute pressure of $1\mathrm{.}50$ atm $.$ Use $g=10\frac{m}{s^2},$ and assume that $1$ atmosphere is $1\mathrm{.}0{10}^{5}Pa.$

$($a$)$ At what speed does the water emerge from the shower head?

$\frac{m}{s}$

$($b$)$ What is the speed of the water in the pipe connected to the pump?

$\frac{m}{s}$

$($c$)$ What is the cross$-$sectional area of the pipe connected to the pump?

$m^2$