Aglass 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 dbot = 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 = 1.20×10-4 s. in this problem, the positive direction is upward.

what is the force that the fist exerts on the top of the bottle?