POSSIBLE SOLUTION(S)

(a) The mass will arrive a the point (5, 0) cm in 3.93 sec.

Input := 

time = 5 Pi/2 / 2//N

Output =


3.92699

(b) We can describe the motion of the mass as a position vector p(t) using circular functions.

(c) To determine when we first see the mass we need to determine the line from the cameraat (10,1) to the circle which is tangent to the circle.

(d) We determine and plot the angle which the line of site of the camera makes with the horizontal as a function of time t.

Input := 

angle[t_] = ArcTan[(p[t][[2]] - 1)/(10 - p[t][[1]] )]

Output =


                  2 t

       -1 + 5 Cos[---]

                   5

ArcTan[---------------]

                  2 t

       10 - 5 Sin[---]

                   5

Input := 

Plot[angle[t],{t,starttime,time}];

(e) We ascertain when the angular velocity and the angular acceleration of the camera is greatest.