An object is orbiting uniformly around a center, has a radius of 1 km, and undergoes an angular displacement of 1° every 0.1 s. What is the position vector (x and y component) of that object at = 1 s if the object starts its motion at x = 1000m, y = 0 m? I'm having trouble understanding this problem for Rotational Physics, any help getting a basis for how to solve this would be greatly appreciated!

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.