After an ice cube is placed in a 10cm glass of lemonade, it sinks to the bottom of the glass in π seconds before the ice

[answerhappygod]

After an ice cube is placed in a 10cm glass of lemonade, itsinks to the bottom of the glass in π seconds before the ice bobsup and down. The ice moves at different speeds!A hypothesis is that the sum of the acceleration of theice, the velocity of the ice cube, and the vertical position of theice in the glass is proportional to e^(−t)+ sin(2t).a. Find a differential equation modeling the vertical position ofthe ice in the glass.b. Find an initial value problem modeling the position of the icein the glass. Be sure to explain your choice of initial conditionsusing words as well as equations.c. Solve the initial value problem.d. What conclusions can we draw about the position of the ice overa long period of time?e. Do you think the hypothesis is correct? Why or why not?