Disgusted and tired of studying, Craig carried his calculus book to the window with the intention of throwing it out. As he gazed out the window, he noticed his calculus instructor walking towards the dorm. Suddenly his plan changed from simply throwing the text out to trying to hit the unsuspecting instructor. Having very little time and wishing to insure a good hit, Craig decided to use his graphing calculator and parametric equations to simulate his throw and determine if he could hit the instructor.
Assuming that the text was thrown from 168 feet high at an angle of 60° with the horizontal with initial velocity of 80 feet per second, Craig wrote the follow parametric equations for the fall of the text:
Supposing that the calculus instructor is walking at a rate of 10 feet per second towards the building and that she is 100 feet away from the building when the book is thrown and further supposing that the instructor is 6 feet tall, Craig's equations for the motion of the instructor are:
Setting his graphing calculator's mode for parametic equations and degrees and for the graphs to be made simultaneously, Craig entered the equations and the following for the viewing window:
t min 0 x min -5 y min -5 t max 2.5 x max 100 y max 200 t step .02 x scl 5 y scl 5
The resulting graph modeled the motion of the book and the instructor. It showed that the book would land in about 1.74 seconds at approximately 69.6 feet from the foot of the building but that the book would miss the calculus instructor. Upset, Craig then began to change the various assumptions of his model so that he could hit the instructor. By the time he had a good model, Craig realized that the instructor had already walked by and that, in trying to relieve his tension in studying calculus, he had had to use calculus!
Can you book the calculus instructor?