HW8-soln - 5.P.73 Throwing from an asteroid (a) Use the...

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5.P.73 Throwing from an asteroid (a) Use the GOAL scheme; Gather, Organize, Analyze, Learn: GATHER: We’re looking for the speed the rock must have just after leaving your hand, such that it goes far away and has a speed of 3 m/s when it is very far away. Note that it will continue in a straight line and at a speed of 3 m/s when it is far away, because the asteroid’s gravitational pull is very small. ORGANIZE: Choose the system to consist of the asteroid and the rock, so that the energy of this combined system does not change. Take the initial state as just after release of the rock, because then there are no exter- nal forces doing work on the system (before release, you do work on that system by pushing the rock). The final state is when the rock is far away. Evidently we should use the energy principle, since we don’t know any- thing about the time but do know something about distances. Let m be the mass of the rock, M the mass of the asteroid. ANALYZE: Ignore change in energy of the asteroid, and there is no change in the rest energy of the rock: Let r f go to infinity, so 1/ r f goes to zero. Multiply by 2/ m to obtain the following: Throw in the direction of the rotation of the asteroid, so that you get an assist from the asteroid’s rotation: you only have to make the speed of the rock relative to you be 15.6 m/s. LEARN: At Cape Canaveral in Florida, rockets are fired eastward over the Atlantic, and discarded boosters fall harmlessly into the sea. The reason for firing eastward is to take advantage of the fact that the Earth rotates eastward, so the rocket has some speed in an “inertial” reference frame even before launch. Similar to the situation in this problem, it costs less to launch eastward than westward.
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HW8-soln - 5.P.73 Throwing from an asteroid (a) Use the...

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