median
don steward
mathematics teaching 10 ~ 16

Wednesday, 23 April 2014

bouncing

this task is from 'five triangles'

what is the gradient of the line so that when a ball bounces (perfectly elastically of course) twice it then hits the mid-point of the lower side of the square?



















some variety of techniques can be used and it doesn't involve higher mathematical techniques
  • trigonometry isn't needed 
  • it can be helpful to have some previous consideration about what happens to the gradient of a line when it is reflected
  • or some consideration of when triangles are similar
  • or you could solve this, very neatly, by working with the 'principle of reflections'
having solved this task, there are some obvious extensions:


















students could also consider the length of the path(s)

No comments: