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Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

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Fill in the blanks with the numbers is a measure of the resistance to flow. a high liquid has a high resistance to flow and flows slowly. the ancients thought everything in the world was made of 4 we now know that there are 94 naturally occurring and scientists have created another 24 i am certain they will create even more. honey flows slowly because it has a high to flowing. a can be separated by physical means because it contains more than one pure substance and 2 pure substances are not chemically bonded to each other. a cannot be separated by physical means. all matter is made up of all elements are with the same number of protons. if it is just a single or many bonded together, if all of them have the same number of protons, it is an element. in a piece of pure iron metal, all the are joined together, that piece of iron metal is called elemental iron. a single of iron is called elemental iron. a mixture has differences from place to place. we might need a microscope to see them or they might be obvious to the unaided eye. there are surfaces separating it into different phases. a mixture is the same everywhere. it is uniform. there are no surfaces separating it into different phases. if different kinds of atoms (different elements) are bonded together by their electrons, it is called a there are physical means of to isolate the different pure substances in a mixture and there are chemical means of to isolate the different elements in a compound. 1. element 2. compound 3. mixture 4. heterogeneous 5. homogeneous 6. pure substance 7. atoms 8. separation 9. viscosity 10. resistance