A glass soda bottle is emptied of soda and filled to the very top with water. A cork is carefully fitted into the top of the bottle, leaving no air between the cork and the water. $($Figure $1)$ ?The top of the bottle has a diameter of Dtop?$=2\mathrm{.}00$ ?cm?and the bottom of the bottle has a diameter of Dbot?$=6\mathrm{.}50$ ?cm?$.$

A student hits the cork sharply with her fist and the bottom of the bottle breaks. The student's fist has a mass of m$=0\mathrm{.}480$ ?kg ?and moves downward at a speed of vi?$=5\mathrm{.}00$ ?m$/$s?$.$ ?It collides elastically with the cork and rebounds at the same speed. The collision lasts for t?$=1\mathrm{.}20\backslash$times $10?4$ ?s?$.$ ?In this problem, the positive direction is upward.

Figure$\mathrm{ 1}$ ?of $1$There is a glass bottle with a cork and a scheme of it on the xy$-$plane. The glass bottle is filled with water to the cork and is oriented along the y axis. The scheme shows the diameters of the top and the bottom of the bottle. They are $2\mathrm{.}0$ ?and $6\mathrm{.}5$ ?centimeters respectively.

Part A What is the force that her fist exerts on the top of the bottle? Express your answer in newtons to three significant figures.

Figure Cork Water, filled to the cork y Diameter of the top = 2.0 cm 1 of 1 Diameter of the bottom = 6.5 cm >