Breaking a Glass Soda Bottle?

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. The top of the bottle has a diameter of D_top = 2.00 cm and the bottom of the bottle has a diameter of D_bot = 6.50 cm. The glass breaks when it is exposed to p_max = 70.0 MPa of pressure.
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 = 0.480 kg and moves downward at a speed of vi = 5.00 m/s. It collides elastically with the cork and rebounds with the same speed. The collision lasts for t = 1.20?0^?4 s. In this problem, the positive direction is upward. What is the force that the fist exerts on the top of the bottle?