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a clyinderical hall has an smooth horizantal floor.a ball is projected along the floor from a point on the wall in an directiom making an angle x with the radius through the point.the ball return 2 the inital points after two impacts with the wallif the coefficent of restution is e,then tan^2x is ans is e^3/e^2+e+1 how can i get this ans

a clyinderical hall has an smooth horizantal floor.a ball is projected along the floor from a point on the wall in an directiom making an angle x with the radius through the point.the ball return 2 the inital points after two impacts with the wallif the coefficent of restution is e,then tan^2x is
ans is e^3/e^2+e+1
how can i get this ans

Grade:

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear jimmyu

let after impact angel made by ball with the radius is y

and after second impact angel made by ball with the radius is z

so 2x+2y+2z =180

or  x+y+z = 90 ........................1

at the first point where ball made first impact

 vsinx = v1siny

and  e = v1cosy /vcosx

 

so e = tanx/tay    or  tany = tanx/e  ...........2

similerly for second impact

      tanz = tany/e  or   tanz = tanx /e2 ............3

 

from equation 1

(90-x) = y+z

or tan(90-x) = tany + tanz /(1-tanytanz)

  1/tanx = (tany + tanz)/(1-tanytanz)

 

put value of  tany and tanz from equation 2and 3

tan2x = e3/(e2 +e +1)

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Badiuddin

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