Consider the situation pictured on the second page. Imagine a two dimensional flat world, S, in which there is no gravity and no friction which is set in 3 dimensional space. It is a fixed horizontal plate described by the coordinate system S (X, Y) where all lengths are in meters and the basis set is Ex , Ey. It origin is O. (The observer at O, called S is not rotating. A circular disk, rotating with angular velocity, @ = (0,0,0) is set on top of S with an observer at its center, o. (His name is s and he is rotating with his frame at angular velocity @. The observer s on the disk uses the rotating frame s(x, y) with basis vectors ex, ey . [This observer (and his instruments rotate with the disk) may or may not know that he is rotating depending on the speed of rotation and the placement of his instruments. ] When you get solutions an important part of this problem is to GRAPH different situations with several different values for o (and bullet speed relative to gun) in order to visualize what observer s would see. (I used my computer BASIC language programming and my HP printer to do this. It took some time...) At time t=0, X axis of O(X,Y) is aligned with the x axis of o(x,y). At time t= 0 the shooter s, standing at point A = (3, 0) on the rotating disk shoots a bullet with vo = (Vox ,Voy ), as measured with respect to o(x,y), which he knows is AIMED DIRECTLY at the target fixed on the disk (with respect to him) at the point B = (1.5, 2.5). The situation in Figure 1 is described below. (a) (10pts) Calculate the path of the bullet in O and explain why O thinks that thrower did not aim correctly. You should state X(t) and Y(t). Remember O sees the observer's gun moving in a circle of radius 3 meters. (b) (40pts) Derive that observer s, in o(x,y), believes the equations for x(t) and y(t) are: x(t)= (xo + voxt)cos(t) + (Voy + @Xo)t sin(ot) y(t) = (xo + voxt)sin(ot) + (voy + 0xo)t cos(wmt) (See Taylor Problem 9.20**) Observer s in o(x,y) is rotating with his reference from o. s may or may not realize he is rotating because may be so small that he doesn't detect it easily.) ()(10pts) Show your thinking is correct by letting = 0. Draw what the observer s sees if vo =(~1.543,2.573) m/s and = 0. Then show graphically that as o is increased in magnitude the bullet misses B by more and more. (Eventually, \"s instruments would tell him that he is rotating and he wouldn't have to imagine a fictious force' causing the deviation of his bullet.) (d)(20pts) Draw a detailed paths of what the observer s sees the bullet follow if he aims the gun directly at point B at time t = 0 (about 59 degrees). Use different combinations of w and vo so that you can compare the resulting paths. Can you estimate the time between the dots in the Figure 1 below. Describe and plot the behavior of the bullet for large valeus of t as seen by observers. - -2 T e _ Sorry, can't divide in separated questions, because to answer b, , and d, you need to do first the questions before them