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SHORT ANSWER. Answer the questions, showingh your work for any calculations. 39) a. Suppose it takes 6 seconds for a 1 kg mass to fall to the ground after being dropped from the top of a tall building. 39) a. If there were no air resistance, so that the mass falls with the acceleration of gravity ge=10 m/s2, about how fast (in m/s) would it be going when it hit the ground? b. The moon's gravity is 1/6 that of earth. If a 2 kg mass falls for 6 seconds on the moon, what speed (in m/s) does it reach? 40) Suppose a star four times more massive than our Sun has a planet the same mass as Earth, orbiting at a distance of 1 AU. a. What is the orbital period P of the planet (in years)? b. Recalling that the earth's speed around the sun is 30 km/s, what is the orbital speed (in km/s) of this planet? c. How would the above answer change if the planet had twice the mass of earth? 7 40) 41) Consider two telescopes with diameters D1= 1 m and D2=10 m. 41) a. What is the ratio of the telescope areas, A2/A1? b. What is the ratio a2/a1 of the smallest angle that can be resolved? 42) A star has a surface temperature that is 5 times that of the sun. a. Recalling that the sun has its spectral energy peak at a wavelength of about 500 nm, what would be the wavelength (in nm) of peak energy of this star? b. What is the surface brightness (energy/area/time) of this star compared to the sun, B/Bsun? 8 42) 43) A spectral line that has rest wavelength of 600 nm is observed in the spectrum of a star to have a wavelength of 600.2 nm. a. Is the star moving away or toward the observer? b. What is the fraction, v/c, the star's speed v to the speed of light c? c. Given that the speed of light is c=300,000 km/s, what is the star's speed in km/s? 9 43)