Ceti is a sun-like star ~ 3.6 pc from earth. assume that an earth- like planet is orbiting t ceti in a circular orbit 1 au from the star. the orbit will subtend a half angle of 0.278". 1 radian 206265" if you have a diffraction limited telescope observing 1u light at maxi- mum elongation, how large would your telescope have to be to produce an image of the system with the image of the star separated from the image of the planet by a dark region at least as large as the image of the star?

If the speed of a particle triples ,by what factor does its kinetic energy increase?

Two objects of different mass start from rest, are pulled by the same magnitude net force, and are moved through the same distance. the work done on object 1 is 900 j. after the force has pulled each object, object 1 moves twice as fast as object 2. how much work is done on object 2?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.