Please help i’m stuck

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.

1. what is the relationship between wavelength and the penetrating power of an electromagnetic wave? a) the penetrating power has no relationship to the wavelength. b) the penetrating power increases as the wavelength increases. c) the penetrating power decreases as the wavelength increases. d) the penetrating power decreases as the wavelength decreases. 2. as ice melts and turns into water, the speed of sound through the material would most likely do what? justify your answer. a) the speed would not change because the material is always water. b) the speed of sound would increase because the density of water is less than that of ice. c) the speed of sound would increase because energy is added to ice in order to make it melt. d) the speed of sound would decrease because sound travels faster through solids than liquids. 3.which of these waves need a medium to travel through? a) sound b) x-rays c) infrared rays d) visible light

One hazard of space travel is debris left by previous missions. there are several thousand masses large enough to detect by radar orbiting the earth, but there are far greater numbers of very small masses such as flakes of paint. calculate the force exerted by a 0.110 mg chip of paint that strikes a space shuttle window at a relative speed of 5.00 ✕ 103 m/s and sticks, given the collision lasts 6.00 ✕ 10-8 s. such a collision chipped the window of the ill-fated challenger in june 1983, causing $50,000 of damage.