Proportionate reasoning Rack and rave In an alternate universe's timeline, NASA has decided to send a rover to the Moon, and agrees with my tweets that rovers should have mini-cannons on them (just because). The Moon is about 1% of Earth's mass, and about 30% of Earth's radius; assume no air resistance. _, a) What is the acceleration due to gravity on the Moon relative to Q as we experience here on Earth? - , \\ - gMoon = 1'1 ) x * gEarth b) If the rover fires a projectile on Earth during testing and it lands after 35 5, how long would the same projectile (launched with the same initial velocity and at the same angle) take to land when fired on the Moon? '315 a; 5 what a drag c) A ball bearing is dropped into a large tank of water. It reaches a terminal speed of 1.4 m/s. [fa ball bearing of the same size and shape but twice the mass is dropped in, what will its terminal speed be? :28 \\-/ m/s d) A spherical ball dropped from a great height reaches a terminal speed of 23 m/s. If a ball of the same surface material and density but twice the radius were dropped from the same height, what will its terminal speed be? 11.5 ] 3.: m/s Heavy questions e) On the surface of a newly discovered exoplanet, an object would weigh 30 N. What would the object weigh on another planet of the same mass but twice the diameter? r 7.5 v' N fis for dumpster fire) A committee has decided to shoot a dumpster full of items representing the year 2020 into the Sun for global catharsis. On the surface of Earth, the dumpster weighs 2800 N. Considering the Sun has a radius of approximately 100x Earth's and a mass about 300,000 times Earth's, how many times heavier would the dumpster be on the Sun? f} Wdumpster, Sun = l 30 J * Wdumpster, Earth I 9) What would the dumpster's weight be on the Sun?* 34000 ]g; N *I know, the Sun doesn't have a solid surface, ' and this is really not an energetically reasonable thing to do, but just go with me on this for a minute