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Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 44.2 km/s and 57.5 km/s. The slower planet's orbital period is 7.50 years.
(a) What is the mass of the star?
kg
(b) What is the orbital period of the faster planet, in years?
A production line inspector wants a mirror that produces an upright image within magnification of 7.4 when it is located 15 mm from a machine part.
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A two-ended "rocket" that is at first stationary on a frictionless floor, with its center an origin of an x axis.
You want to shoot a 19cm long arrow parallel to this axle and through the wheel without hitting any of spokes. Suppose that the arrow and the spokes are very thin.
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