Consider a ball (with moment of inertia i=2/5mr^2) which bounces elastically off a surface. assume that the ball’s speed in the direction perpendicular to the surface is the same before and after a bounce. also, assume that the ball is made of a type of rubber which allows it to not slip on the surface (which has friction) during the bounce. (this implies that the angular and linear motions may affect each other.)the ball is projected from the surface of a plane which is inclined at angle θ.the initial velocity of the ball is perpendicular to the plane and has magnitude v. the initial angular velocity is zero. find the component of the ball’s velocity along the plane, immediately after thenth bounce.

vn = 10nV tanθ 7 (n even), and vn = (10n−4) V tanθ 7 (n odd).

idk the answer, it is hard

do you have a formula possibly

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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