A particle moves on the inside of a fixed, smooth vertical hoop of radius R. It

Question

A particle moves on the inside of a fixed, smooth vertical hoop of radius R. It is projected from the lowest point A with the velocity 2 (a) Show that it will lave the hoop at a heightR above A and meet the hoop again at A. DO NOT WORK BACKWARDS FROM THE GIVEN ANSWER (3 pts) Determine the trajectory of the particle y(x) once it leaves the hoop. Use only the coordinate system shown in the figure. (2 pt) (b) (x) = c)Let the radius R -40 m. Using Excel, graph (i) the hoop and (ii) the trajectory of the particle from point A when projected till it returns to point A Print your file and also Email me your file. (2 pts) (d) What is the velocity of the particle in vector form just before its impact at A? (1 pt) (ii) What was its airborne time in seconds to two decimal places? (1 pt) airborne (ii) What was the maximum height in meters of the particle above point A? (1 pt) Write your answer to two decimal places. max

Explanation / Answer

Ps: Answer readability may be poor since I used MS Word to type. Sorry for inconvenience

When the particle leaves the hoop the velocity will be

                                    V=((1/2)Rg(3)1/2 )1/2

               R: radius of the loop

         g: acceleration due to gravity

now consider the particle leaves the hoop at an angle 30 degree w.r.t the horizontal axis then, it follows a parabolic path

y=xtan30- gx2/(2v2cos230)

   =x/31/2 -gx2/{2*[(1/2)Rg(3)1/2 ](31/2/2)2}

Y(x) = x/31/2-4x2/{33/2R}

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