FYKOS Year 35 Series 4 Problem 2 — Freeway · FYKOS 35 #35.4.2
Physics · mechanics
Problem
Besides designing its own beer, the Faculty of Mathematics and Physics plans to build an amusement park. They intend to create a unique physics-themed bobsleigh track, where the sleigh starts with non-zero vertical velocity vy and starts moving directly downwards. The track gradually curves towards the horizontal direction, while the vertical component of the velocity remains constant. What is the dependence of sleigh's horizontal velocity component on the decline in height? And what is the dependence of the magnitude of velocity on time? Assume the sleigh moves on the track without friction.
Bonus What is the shape of the coaster?