Classical mechanics problem

A ball of very small size is dropped vertically onto a frictionless inclined plane which makes an angle thetha with the horizontal. Initially the distance between the plane and the ball is d and the speed of the ball is zero. The trajectory of the ball consists of parabolic arcs .what will be the locus of all those focus of all those parabolic arcs . Assume that elastic collisions is taking place and no air resistance is there

#Mechanics

Easy Math Editor

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Comments

Here is a plot of a ball dropped onto a 30 degree ramp from a height of 1 meter. The key to the simulation is that upon every bounce, the component of the velocity normal to the ramp is reversed, and the component of the velocity tangential to the ramp is preserved.

The second graph is of a ball dropped onto a 15 degree ramp from a height of 5 meters

Steven Chase - 2 years, 3 months ago

Sir is it possible to join the focus of all these parabolas in the figure ? Also sir can u make a horizontal straight line passing through from the initial position ? So now from this property ( which is directrix is same horizontal line for all the parabolas) isn't it possible to easily get the locus in mathematical way sir ?? Or now also its complicated ? @Steven Chase sir if yes then I will make another problem , from this next onwards. My friends told me that focus has a nice locus . They maybe wrong though.